# setwd("C:/Users/Student/OneDrive/DS-3001/")

df <- read.csv("SpotifyFeatures.csv")

table(df$genre)
## 
##        A Capella      Alternative            Anime            Blues 
##              119             9263             8936             9023 
## Children's Music Children’s Music        Classical           Comedy 
##             5403             9353             9256             9681 
##          Country            Dance       Electronic             Folk 
##             8664             8701             9377             9299 
##          Hip-Hop            Indie             Jazz            Movie 
##             9295             9543             9441             7806 
##            Opera              Pop              R&B              Rap 
##             8280             9386             8992             9232 
##           Reggae        Reggaeton             Rock              Ska 
##             8771             8927             9272             8874 
##             Soul       Soundtrack            World 
##             9089             9646             9096
df2 <-unique(df)
#art_freq <- as.data.frame(table(df2$artist_name))
#df3 <- df2[df2$artist_name == 'Drake',]
#final_pop <- df3[-c(1, 2, 3, 4)]
final_pop <- df2[-c(1, 2, 3, 4)]

Finish any other data prep (one-hot encode, reduce factor levels)

factor_cols <- c(7, 10, 13)
final_pop[,factor_cols] <- lapply(final_pop[,factor_cols], as_factor)
final_pop$duration_ms <- as.numeric(final_pop$duration_ms)
final_pop$popularity <- as.numeric(final_pop$popularity)

correlationMatrix <- cor(final_pop[, sapply(final_pop, is.numeric)], use = "complete.obs", method="pearson")
corrplot(correlationMatrix, method = 'number')

Create test and training sets

sample_rows = 1:nrow(final_pop)

# sample() is a randomized function, use set.seed() to make your results reproducible.
set.seed(1984) #sample(x, size, replace = FALSE, prob = NULL)
test_rows = sample(sample_rows,
                   dim(final_pop)[1]*.10, #start with 10% of our dataset, could do 20%
                   # but random forest does require more training data because of the 
                   # sampling so 90% might be a better approach with this small of a dataset
                   replace = FALSE)# We don't want duplicate samples


pop_train = final_pop[-test_rows,]
pop_test = final_pop[test_rows,]

Calculate the initial mtry level

dim(pop_train)
## [1] 209453     14
mytry_tune <- function(x){
  xx <- dim(x)[2]-1
  sqrt(xx)
}


mytry_tune(final_pop)
## [1] 3.605551

Run the initial RF model with 1000 trees

pop_RF = randomForest(as.numeric(popularity)~.,          #<- Formula: response variable ~ predictors.
                            #   The period means 'use all other variables in the data'.
                            pop_train,     #<- A data frame with the variables to be used.
                            #y = NULL,           #<- A response vector. This is unnecessary because we're specifying a response formula.
                            #subset = NULL,      #<- This is unnecessary because we're using all the rows in the training data set.
                            #xtest = NULL,       #<- This is already defined in the formula by the ".".
                            #ytest = NULL,       #<- This is already defined in the formula by "PREGNANT".
                            ntree = 1000,        #<- Number of trees to grow. This should not be set to too small a number, to ensure that every input row gets classified at least a few times.
                            mtry = 4,            #<- Number of variables randomly sampled as candidates at each split. Default number for classification is sqrt(# of variables). Default number for regression is (# of variables / 3).
                            replace = TRUE,      #<- Should sampled data points be replaced.
                            #classwt = NULL,     #<- Priors of the classes. Use this if you want to specify what proportion of the data SHOULD be in each class. This is relevant if your sample data is not completely representative of the actual population 
                            #strata = NULL,      #<- Not necessary for our purpose here.
                            sampsize = 100,      #<- Size of sample to draw each time.
                            nodesize = 5,        #<- Minimum numbers of data points in terminal nodes.
                            #maxnodes = NULL,    #<- Limits the number of maximum splits. 
                            importance = TRUE,   #<- Should importance of predictors be assessed?
                            #localImp = FALSE,   #<- Should casewise importance measure be computed? (Setting this to TRUE will override importance.)
                            proximity = FALSE,    #<- Should a proximity measure between rows be calculated?
                            norm.votes = TRUE,   #<- If TRUE (default), the final result of votes are expressed as fractions. If FALSE, raw vote counts are returned (useful for combining results from different runs).
                            do.trace = TRUE,     #<- If set to TRUE, give a more verbose output as randomForest is run.
                            keep.forest = TRUE,  #<- If set to FALSE, the forest will not be retained in the output object. If xtest is given, defaults to FALSE.
                            keep.inbag = TRUE)   #<- Should an n by ntree matrix be returned that keeps track of which samples are in-bag in which trees? 
##      |      Out-of-bag   |
## Tree |      MSE  %Var(y) |
##    1 |    498.1   150.46 |
##    2 |    366.1   110.58 |
##    3 |    332.1   100.31 |
##    4 |    305.8    92.37 |
##    5 |    299.2    90.38 |
##    6 |    286.3    86.47 |
##    7 |    276.7    83.58 |
##    8 |    271.7    82.06 |
##    9 |    265.8    80.27 |
##   10 |    263.9    79.71 |
##   11 |    263.1    79.47 |
##   12 |    258.5    78.07 |
##   13 |    256.6    77.52 |
##   14 |    257.2    77.67 |
##   15 |    255.4    77.15 |
##   16 |    255.2    77.07 |
##   17 |    253.7    76.62 |
##   18 |    252.7    76.33 |
##   19 |    251.6    75.99 |
##   20 |      250    75.51 |
##   21 |    250.3    75.59 |
##   22 |    249.5    75.36 |
##   23 |      248    74.91 |
##   24 |    247.3    74.70 |
##   25 |    247.4    74.73 |
##   26 |    246.8    74.53 |
##   27 |    246.4    74.42 |
##   28 |    246.1    74.33 |
##   29 |    245.7    74.20 |
##   30 |      246    74.31 |
##   31 |    245.6    74.20 |
##   32 |    244.9    73.98 |
##   33 |    244.8    73.95 |
##   34 |    244.7    73.90 |
##   35 |    244.9    73.97 |
##   36 |    244.6    73.88 |
##   37 |    244.2    73.76 |
##   38 |    243.9    73.66 |
##   39 |    243.9    73.67 |
##   40 |    244.2    73.76 |
##   41 |    243.9    73.66 |
##   42 |    243.9    73.68 |
##   43 |    243.8    73.63 |
##   44 |    243.9    73.67 |
##   45 |    243.4    73.51 |
##   46 |    243.2    73.47 |
##   47 |    243.5    73.56 |
##   48 |    243.6    73.57 |
##   49 |    243.3    73.50 |
##   50 |    243.5    73.55 |
##   51 |    243.6    73.58 |
##   52 |    243.5    73.55 |
##   53 |    243.4    73.52 |
##   54 |    243.6    73.57 |
##   55 |    243.5    73.55 |
##   56 |    243.1    73.42 |
##   57 |    242.9    73.37 |
##   58 |    242.7    73.31 |
##   59 |    242.9    73.36 |
##   60 |    242.8    73.33 |
##   61 |    242.8    73.34 |
##   62 |    242.8    73.34 |
##   63 |    242.7    73.29 |
##   64 |    242.7    73.32 |
##   65 |    242.6    73.28 |
##   66 |    242.5    73.24 |
##   67 |    242.6    73.28 |
##   68 |    242.4    73.23 |
##   69 |    242.3    73.18 |
##   70 |    242.4    73.21 |
##   71 |    241.9    73.07 |
##   72 |    241.6    72.97 |
##   73 |    241.4    72.93 |
##   74 |    241.3    72.89 |
##   75 |    241.4    72.91 |
##   76 |    241.5    72.94 |
##   77 |    241.5    72.93 |
##   78 |    241.6    72.98 |
##   79 |    241.3    72.87 |
##   80 |    241.4    72.92 |
##   81 |    241.3    72.88 |
##   82 |    241.2    72.85 |
##   83 |    241.2    72.86 |
##   84 |    241.2    72.87 |
##   85 |      241    72.81 |
##   86 |    240.8    72.74 |
##   87 |    240.8    72.72 |
##   88 |    240.7    72.71 |
##   89 |    240.4    72.62 |
##   90 |    240.5    72.63 |
##   91 |    240.5    72.64 |
##   92 |    240.3    72.58 |
##   93 |    240.3    72.59 |
##   94 |    240.2    72.56 |
##   95 |    240.1    72.52 |
##   96 |    240.1    72.51 |
##   97 |    240.1    72.51 |
##   98 |    239.9    72.46 |
##   99 |    239.9    72.46 |
##  100 |    239.8    72.43 |
##  101 |    239.8    72.45 |
##  102 |      240    72.48 |
##  103 |      240    72.48 |
##  104 |    239.9    72.48 |
##  105 |    239.9    72.46 |
##  106 |    239.9    72.46 |
##  107 |    239.9    72.46 |
##  108 |      240    72.49 |
##  109 |    239.9    72.46 |
##  110 |    239.8    72.42 |
##  111 |    239.9    72.46 |
##  112 |    239.8    72.42 |
##  113 |    239.9    72.47 |
##  114 |    239.7    72.41 |
##  115 |    239.8    72.43 |
##  116 |    239.8    72.43 |
##  117 |    239.9    72.46 |
##  118 |    239.7    72.40 |
##  119 |    239.7    72.41 |
##  120 |    239.8    72.44 |
##  121 |    239.7    72.39 |
##  122 |    239.6    72.36 |
##  123 |    239.5    72.33 |
##  124 |    239.3    72.29 |
##  125 |    239.3    72.27 |
##  126 |    239.3    72.27 |
##  127 |    239.4    72.32 |
##  128 |    239.4    72.30 |
##  129 |    239.2    72.26 |
##  130 |    239.3    72.28 |
##  131 |    239.3    72.27 |
##  132 |    239.4    72.31 |
##  133 |    239.4    72.33 |
##  134 |    239.5    72.36 |
##  135 |    239.5    72.33 |
##  136 |    239.3    72.28 |
##  137 |    239.3    72.29 |
##  138 |    239.3    72.29 |
##  139 |    239.4    72.30 |
##  140 |    239.4    72.32 |
##  141 |    239.6    72.36 |
##  142 |    239.6    72.37 |
##  143 |    239.5    72.35 |
##  144 |    239.5    72.35 |
##  145 |    239.6    72.36 |
##  146 |    239.4    72.32 |
##  147 |    239.4    72.32 |
##  148 |    239.4    72.32 |
##  149 |    239.4    72.31 |
##  150 |    239.3    72.28 |
##  151 |    239.4    72.31 |
##  152 |    239.5    72.33 |
##  153 |    239.3    72.29 |
##  154 |    239.3    72.28 |
##  155 |    239.2    72.26 |
##  156 |    239.1    72.23 |
##  157 |    239.1    72.23 |
##  158 |    239.1    72.21 |
##  159 |    239.2    72.25 |
##  160 |    239.1    72.22 |
##  161 |    239.1    72.23 |
##  162 |    239.2    72.25 |
##  163 |      239    72.19 |
##  164 |    238.9    72.17 |
##  165 |    238.8    72.14 |
##  166 |    238.9    72.17 |
##  167 |      239    72.19 |
##  168 |    239.1    72.22 |
##  169 |    239.1    72.23 |
##  170 |    239.1    72.21 |
##  171 |      239    72.20 |
##  172 |      239    72.19 |
##  173 |      239    72.20 |
##  174 |    239.1    72.22 |
##  175 |      239    72.20 |
##  176 |    239.1    72.22 |
##  177 |      239    72.19 |
##  178 |      239    72.18 |
##  179 |      239    72.18 |
##  180 |    238.9    72.17 |
##  181 |    239.1    72.21 |
##  182 |    239.1    72.22 |
##  183 |    239.1    72.22 |
##  184 |    239.2    72.24 |
##  185 |    239.2    72.24 |
##  186 |    239.2    72.25 |
##  187 |    239.2    72.25 |
##  188 |    239.2    72.24 |
##  189 |    239.2    72.26 |
##  190 |    239.3    72.27 |
##  191 |    239.4    72.31 |
##  192 |    239.4    72.33 |
##  193 |    239.4    72.32 |
##  194 |    239.4    72.30 |
##  195 |    239.3    72.29 |
##  196 |    239.4    72.30 |
##  197 |    239.3    72.29 |
##  198 |    239.3    72.27 |
##  199 |    239.4    72.30 |
##  200 |    239.3    72.29 |
##  201 |    239.2    72.26 |
##  202 |    239.2    72.26 |
##  203 |    239.2    72.25 |
##  204 |    239.2    72.26 |
##  205 |    239.3    72.27 |
##  206 |    239.2    72.26 |
##  207 |    239.3    72.28 |
##  208 |    239.4    72.30 |
##  209 |    239.3    72.28 |
##  210 |    239.4    72.31 |
##  211 |    239.4    72.32 |
##  212 |    239.5    72.34 |
##  213 |    239.6    72.37 |
##  214 |    239.6    72.37 |
##  215 |    239.6    72.37 |
##  216 |    239.7    72.39 |
##  217 |    239.6    72.36 |
##  218 |    239.6    72.37 |
##  219 |    239.6    72.38 |
##  220 |    239.5    72.33 |
##  221 |    239.6    72.36 |
##  222 |    239.6    72.36 |
##  223 |    239.7    72.39 |
##  224 |    239.7    72.40 |
##  225 |    239.7    72.42 |
##  226 |    239.8    72.42 |
##  227 |    239.7    72.41 |
##  228 |    239.7    72.41 |
##  229 |    239.8    72.42 |
##  230 |    239.8    72.42 |
##  231 |    239.8    72.42 |
##  232 |    239.7    72.40 |
##  233 |    239.6    72.38 |
##  234 |    239.7    72.39 |
##  235 |    239.6    72.38 |
##  236 |    239.6    72.36 |
##  237 |    239.6    72.37 |
##  238 |    239.6    72.38 |
##  239 |    239.7    72.39 |
##  240 |    239.7    72.39 |
##  241 |    239.6    72.39 |
##  242 |    239.7    72.40 |
##  243 |    239.7    72.39 |
##  244 |    239.6    72.38 |
##  245 |    239.7    72.39 |
##  246 |    239.7    72.40 |
##  247 |    239.6    72.38 |
##  248 |    239.6    72.37 |
##  249 |    239.6    72.36 |
##  250 |    239.5    72.35 |
##  251 |    239.5    72.34 |
##  252 |    239.6    72.36 |
##  253 |    239.5    72.35 |
##  254 |    239.4    72.31 |
##  255 |    239.4    72.31 |
##  256 |    239.4    72.30 |
##  257 |    239.4    72.30 |
##  258 |    239.4    72.32 |
##  259 |    239.4    72.31 |
##  260 |    239.3    72.29 |
##  261 |    239.4    72.30 |
##  262 |    239.3    72.27 |
##  263 |    239.2    72.27 |
##  264 |    239.3    72.27 |
##  265 |    239.2    72.25 |
##  266 |    239.2    72.25 |
##  267 |    239.2    72.25 |
##  268 |    239.2    72.24 |
##  269 |    239.2    72.26 |
##  270 |    239.3    72.29 |
##  271 |    239.3    72.27 |
##  272 |    239.3    72.28 |
##  273 |    239.4    72.30 |
##  274 |    239.4    72.31 |
##  275 |    239.4    72.30 |
##  276 |    239.3    72.28 |
##  277 |    239.3    72.27 |
##  278 |    239.2    72.26 |
##  279 |    239.2    72.25 |
##  280 |    239.2    72.24 |
##  281 |    239.2    72.26 |
##  282 |    239.3    72.27 |
##  283 |    239.4    72.31 |
##  284 |    239.4    72.31 |
##  285 |    239.3    72.29 |
##  286 |    239.3    72.29 |
##  287 |    239.3    72.28 |
##  288 |    239.2    72.26 |
##  289 |    239.2    72.25 |
##  290 |    239.2    72.24 |
##  291 |    239.1    72.23 |
##  292 |    239.1    72.22 |
##  293 |    239.1    72.23 |
##  294 |    239.1    72.23 |
##  295 |    239.2    72.25 |
##  296 |    239.2    72.26 |
##  297 |    239.2    72.26 |
##  298 |    239.3    72.28 |
##  299 |    239.3    72.28 |
##  300 |    239.3    72.29 |
##  301 |    239.4    72.30 |
##  302 |    239.3    72.29 |
##  303 |    239.4    72.30 |
##  304 |    239.4    72.31 |
##  305 |    239.4    72.31 |
##  306 |    239.4    72.31 |
##  307 |    239.5    72.34 |
##  308 |    239.5    72.35 |
##  309 |    239.6    72.37 |
##  310 |    239.6    72.37 |
##  311 |    239.7    72.39 |
##  312 |    239.7    72.40 |
##  313 |    239.7    72.41 |
##  314 |    239.7    72.39 |
##  315 |    239.6    72.38 |
##  316 |    239.7    72.40 |
##  317 |    239.7    72.41 |
##  318 |    239.7    72.40 |
##  319 |    239.7    72.40 |
##  320 |    239.7    72.41 |
##  321 |    239.7    72.40 |
##  322 |    239.7    72.40 |
##  323 |    239.7    72.41 |
##  324 |    239.7    72.41 |
##  325 |    239.8    72.42 |
##  326 |    239.7    72.41 |
##  327 |    239.7    72.40 |
##  328 |    239.7    72.40 |
##  329 |    239.6    72.38 |
##  330 |    239.7    72.39 |
##  331 |    239.7    72.41 |
##  332 |    239.7    72.39 |
##  333 |    239.6    72.37 |
##  334 |    239.6    72.36 |
##  335 |    239.5    72.34 |
##  336 |    239.5    72.34 |
##  337 |    239.4    72.32 |
##  338 |    239.4    72.31 |
##  339 |    239.4    72.31 |
##  340 |    239.4    72.30 |
##  341 |    239.4    72.31 |
##  342 |    239.4    72.31 |
##  343 |    239.4    72.31 |
##  344 |    239.4    72.31 |
##  345 |    239.4    72.31 |
##  346 |    239.4    72.32 |
##  347 |    239.4    72.32 |
##  348 |    239.4    72.32 |
##  349 |    239.4    72.31 |
##  350 |    239.4    72.31 |
##  351 |    239.4    72.31 |
##  352 |    239.4    72.30 |
##  353 |    239.3    72.28 |
##  354 |    239.2    72.26 |
##  355 |    239.2    72.26 |
##  356 |    239.3    72.27 |
##  357 |    239.3    72.27 |
##  358 |    239.3    72.29 |
##  359 |    239.4    72.31 |
##  360 |    239.4    72.30 |
##  361 |    239.4    72.31 |
##  362 |    239.4    72.30 |
##  363 |    239.4    72.30 |
##  364 |    239.4    72.32 |
##  365 |    239.5    72.34 |
##  366 |    239.5    72.33 |
##  367 |    239.4    72.32 |
##  368 |    239.4    72.32 |
##  369 |    239.4    72.31 |
##  370 |    239.5    72.33 |
##  371 |    239.5    72.35 |
##  372 |    239.5    72.35 |
##  373 |    239.5    72.33 |
##  374 |    239.5    72.33 |
##  375 |    239.5    72.34 |
##  376 |    239.5    72.34 |
##  377 |    239.5    72.34 |
##  378 |    239.5    72.34 |
##  379 |    239.4    72.32 |
##  380 |    239.4    72.31 |
##  381 |    239.5    72.33 |
##  382 |    239.5    72.34 |
##  383 |    239.5    72.33 |
##  384 |    239.5    72.33 |
##  385 |    239.5    72.33 |
##  386 |    239.4    72.32 |
##  387 |    239.5    72.33 |
##  388 |    239.5    72.33 |
##  389 |    239.4    72.32 |
##  390 |    239.4    72.32 |
##  391 |    239.4    72.32 |
##  392 |    239.5    72.33 |
##  393 |    239.5    72.33 |
##  394 |    239.5    72.34 |
##  395 |    239.5    72.36 |
##  396 |    239.6    72.37 |
##  397 |    239.6    72.37 |
##  398 |    239.6    72.38 |
##  399 |    239.6    72.37 |
##  400 |    239.6    72.38 |
##  401 |    239.6    72.37 |
##  402 |    239.5    72.36 |
##  403 |    239.6    72.37 |
##  404 |    239.7    72.40 |
##  405 |    239.7    72.41 |
##  406 |    239.7    72.40 |
##  407 |    239.7    72.39 |
##  408 |    239.7    72.40 |
##  409 |    239.7    72.40 |
##  410 |    239.6    72.38 |
##  411 |    239.6    72.37 |
##  412 |    239.6    72.38 |
##  413 |    239.6    72.38 |
##  414 |    239.6    72.38 |
##  415 |    239.6    72.38 |
##  416 |    239.7    72.40 |
##  417 |    239.7    72.39 |
##  418 |    239.7    72.40 |
##  419 |    239.7    72.41 |
##  420 |    239.7    72.39 |
##  421 |    239.7    72.39 |
##  422 |    239.7    72.40 |
##  423 |    239.7    72.40 |
##  424 |    239.7    72.40 |
##  425 |    239.7    72.41 |
##  426 |    239.8    72.43 |
##  427 |    239.8    72.43 |
##  428 |    239.8    72.43 |
##  429 |    239.8    72.44 |
##  430 |    239.9    72.45 |
##  431 |    239.9    72.45 |
##  432 |    239.8    72.44 |
##  433 |    239.9    72.45 |
##  434 |    239.9    72.47 |
##  435 |    239.9    72.47 |
##  436 |      240    72.48 |
##  437 |      240    72.49 |
##  438 |      240    72.48 |
##  439 |    239.9    72.47 |
##  440 |    239.9    72.47 |
##  441 |    239.9    72.46 |
##  442 |    239.9    72.47 |
##  443 |    239.9    72.47 |
##  444 |    239.9    72.46 |
##  445 |    239.9    72.46 |
##  446 |    239.9    72.46 |
##  447 |    239.9    72.45 |
##  448 |    239.9    72.45 |
##  449 |    239.9    72.45 |
##  450 |    239.8    72.44 |
##  451 |    239.8    72.43 |
##  452 |    239.8    72.42 |
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##  821 |    239.4    72.31 |
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##  824 |    239.4    72.30 |
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##  826 |    239.3    72.29 |
##  827 |    239.4    72.30 |
##  828 |    239.3    72.29 |
##  829 |    239.3    72.29 |
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##  833 |    239.3    72.28 |
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##  835 |    239.3    72.27 |
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##  844 |    239.2    72.25 |
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##  899 |    239.2    72.24 |
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##  901 |    239.2    72.25 |
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##  914 |    239.1    72.23 |
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##  916 |    239.1    72.22 |
##  917 |    239.1    72.22 |
##  918 |    239.1    72.22 |
##  919 |    239.1    72.21 |
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##  921 |    239.1    72.22 |
##  922 |    239.1    72.22 |
##  923 |    239.1    72.23 |
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##  927 |    239.1    72.23 |
##  928 |    239.1    72.23 |
##  929 |    239.1    72.22 |
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##  931 |    239.1    72.23 |
##  932 |    239.1    72.23 |
##  933 |    239.1    72.23 |
##  934 |    239.1    72.23 |
##  935 |    239.1    72.23 |
##  936 |    239.2    72.24 |
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##  938 |    239.2    72.24 |
##  939 |    239.1    72.23 |
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##  941 |    239.1    72.23 |
##  942 |    239.2    72.24 |
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##  944 |    239.2    72.24 |
##  945 |    239.1    72.23 |
##  946 |    239.1    72.22 |
##  947 |    239.1    72.22 |
##  948 |    239.1    72.22 |
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##  961 |    239.1    72.22 |
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##  966 |    239.1    72.22 |
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##  968 |    239.1    72.22 |
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##  971 |    239.1    72.23 |
##  972 |    239.1    72.23 |
##  973 |    239.1    72.22 |
##  974 |    239.1    72.22 |
##  975 |    239.1    72.22 |
##  976 |    239.1    72.22 |
##  977 |    239.1    72.22 |
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##  979 |    239.1    72.21 |
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##  981 |    239.1    72.21 |
##  982 |    239.1    72.21 |
##  983 |    239.1    72.21 |
##  984 |    239.1    72.21 |
##  985 |    239.1    72.21 |
##  986 |    239.1    72.21 |
##  987 |    239.1    72.21 |
##  988 |    239.1    72.21 |
##  989 |    239.1    72.21 |
##  990 |    239.1    72.21 |
##  991 |      239    72.20 |
##  992 |      239    72.20 |
##  993 |      239    72.20 |
##  994 |      239    72.20 |
##  995 |      239    72.20 |
##  996 |      239    72.20 |
##  997 |      239    72.20 |
##  998 |      239    72.19 |
##  999 |      239    72.19 |
## 1000 |      239    72.19 |
#==================================================================================

####  Random forest output ####

# Calculate the RMSE
sqrt(pop_RF$mse[length(pop_RF$mse)])
## [1] 15.4595
# The "predicted" argument contains a vector of predictions for each 
# data point.
as.data.frame(pop_RF$predicted)
##        pop_RF$predicted
## 1              34.67064
## 2              42.81718
## 3              31.44826
## 4              37.08677
## 5              24.38450
## 6              32.38774
## 7              39.61924
## 8              39.36617
## 9              47.32925
## 10             41.80318
## 11             29.28222
## 12             32.35883
## 13             47.80965
## 14             31.89263
## 15             29.19882
## 16             32.14890
## 17             31.00622
## 18             41.51845
## 19             44.62968
## 20             48.30445
## 21             41.18572
## 22             41.71563
## 23             39.60464
## 24             32.15645
## 25             43.22125
## 26             28.55773
## 27             46.99363
## 28             36.13585
## 29             30.42890
## 30             42.29467
## 31             44.53170
## 32             29.31971
## 33             30.70998
## 34             31.99785
## 35             41.05518
## 36             36.76093
## 37             49.78075
## 38             39.70494
## 39             29.01297
## 40             37.33515
## 42             28.75349
## 43             28.18772
## 44             36.51198
## 45             38.43065
## 46             35.84293
## 47             46.50655
## 49             41.65879
## 50             35.17183
## 51             31.52527
## 52             35.01907
## 53             28.27907
## 54             38.32169
## 55             22.88817
## 56             25.76938
## 57             29.27420
## 58             31.42850
## 59             27.79207
## 61             26.91860
## 63             27.00322
## 64             39.51780
## 65             38.00262
## 66             45.13122
## 68             31.32918
## 69             34.12217
## 70             36.43615
## 71             28.04758
## 72             35.40977
## 73             25.52642
## 74             32.17085
## 75             31.01498
## 77             31.08262
## 78             34.81590
## 80             28.92130
## 81             45.92356
## 82             33.53832
## 83             32.99459
## 84             29.84237
## 85             36.04850
## 86             34.93158
## 87             37.31143
## 88             40.40182
## 89             42.35324
## 90             45.26855
## 92             40.19078
## 93             47.27050
## 94             32.54597
## 95             42.45165
## 96             39.29803
## 97             35.76750
## 99             27.91428
## 100            47.97434
## 101            42.44506
## 102            28.06575
## 103            26.99498
## 104            44.61133
## 105            36.32536
## 106            38.32807
## 107            30.85378
## 108            45.42853
## 109            37.16256
## 110            39.80832
## 111            41.15920
## 112            41.48513
## 113            40.81883
## 114            29.71495
## 116            40.81304
## 117            49.28767
## 118            32.78492
## 119            46.99245
## 120            28.90599
## 121            33.06793
## 122            34.36638
## 123            35.26508
## 124            38.45548
## 125            41.66680
## 126            31.08612
## 127            37.84720
## 128            48.68737
## 129            28.15155
## 130            35.15763
## 131            25.75852
## 132            33.78173
## 133            28.02100
## 134            27.88418
## 135            45.71493
## 136            48.66305
## 137            49.49422
## 138            49.91698
## 140            49.21300
## 141            41.46563
## 142            45.88945
## 143            34.52072
## 144            42.61268
## 145            46.33614
## 146            44.17694
## 147            48.52667
## 148            51.08093
## 149            52.80890
## 150            46.02410
## 152            45.69731
## 153            49.69340
## 154            40.92580
## 155            45.26305
## 156            47.64777
## 157            51.34591
## 158            50.24867
## 159            39.12785
## 160            45.72003
## 161            47.74683
## 162            49.00275
## 163            43.99263
## 164            45.62538
## 165            46.26988
## 166            50.00434
## 167            48.11472
## 168            47.61215
## 169            51.57353
## 170            50.88127
## 171            48.23092
## 173            46.69102
## 174            40.47148
## 176            46.09347
## 177            46.49144
## 178            46.77963
## 179            46.06044
## 180            41.23342
## 181            48.55237
## 182            50.12650
## 183            46.74145
## 184            47.72248
## 185            49.68635
## 186            49.36143
## 187            49.48350
## 188            43.75337
## 189            50.23428
## 190            44.53133
## 191            47.58795
## 192            38.12767
## 193            47.12793
## 194            47.89958
## 195            48.92534
## 196            48.70217
## 197            46.76822
## 198            49.42555
## 199            47.93953
## 203            47.18403
## 204            48.10140
## 205            49.72375
## 206            49.60977
## 207            50.47034
## 208            49.24852
## 209            45.98200
## 210            48.50803
## 211            42.95846
## 212            51.29085
## 213            45.29072
## 214            43.46402
## 215            51.53450
## 216            43.03692
## 217            52.41785
## 218            43.18955
## 219            49.85580
## 220            38.97495
## 221            51.23397
## 222            48.49648
## 223            40.43212
## 224            48.82868
## 225            47.60742
## 226            48.85528
## 227            47.85502
## 228            48.45985
## 229            44.64645
## 230            53.23417
## 231            50.44145
## 232            43.25362
## 233            50.84305
## 235            39.18063
## 236            38.48688
## 237            38.46892
## 238            46.52400
## 239            42.05768
## 241            51.12493
## 242            48.76912
## 244            46.35938
## 245            49.74693
## 246            48.98503
## 247            40.11892
## 248            48.81473
## 249            46.40398
## 250            48.59027
## 251            45.44891
## 252            49.31842
## 253            49.15463
## 254            50.25998
## 255            49.32581
## 256            47.49860
## 257            50.57099
## 258            48.60250
## 259            47.88420
## 260            52.12478
## 261            46.73697
## 262            48.30347
## 263            50.47022
## 264            48.12478
## 265            40.63856
## 266            33.32596
## 267            48.21672
## 268            48.30383
## 269            46.57162
## 270            52.41752
## 271            38.62315
## 272            47.06525
## 273            50.55281
## 274            49.44313
## 275            42.41388
## 276            44.80746
## 277            49.43173
## 278            39.32107
## 279            49.79997
## 280            38.93890
## 281            42.01222
## 282            26.86820
## 283            28.84500
## 284            27.28415
## 286            23.45973
## 287            39.90272
## 288            27.85470
## 290            46.39441
## 291            46.07513
## 294            28.17474
## 295            33.54407
## 296            26.97128
## 297            48.51417
## 298            27.26995
## 299            44.66697
## 300            46.70148
## 301            24.41456
## 302            28.70265
## 303            25.17933
## 304            38.36725
## 305            36.15317
## 306            41.01421
## 307            27.98594
## 308            35.49341
## 309            28.52114
## 310            42.18362
## 311            45.85985
## 312            26.86813
## 313            40.97727
## 314            45.24149
## 315            25.05843
## 317            35.16928
## 318            29.17968
## 319            33.98400
## 321            39.60843
## 322            39.83312
## 323            32.15300
## 324            38.04837
## 326            38.55853
## 327            35.57281
## 328            46.16883
## 329            32.51723
## 330            42.80806
## 331            43.11635
## 332            42.87319
## 333            27.37633
## 334            38.84676
## 335            26.76395
## 336            27.39527
## 337            31.23902
## 338            30.88387
## 339            28.51842
## 340            40.97692
## 341            34.89047
## 342            26.51270
## 343            30.85648
## 345            28.15347
## 346            46.76673
## 347            32.56713
## 349            44.76565
## 350            30.04505
## 351            40.20325
## 352            26.52119
## 353            46.48871
## 354            32.74593
## 356            28.85543
## 358            33.28573
## 359            34.83725
## 360            44.40712
## 361            37.79255
## 362            37.47823
## 363            33.11553
## 364            38.64198
## 365            24.69368
## 367            47.88838
## 368            28.80853
## 369            42.85517
## 372            45.78263
## 373            26.68775
## 374            38.35935
## 375            34.13961
## 377            38.66094
## 378            31.51882
## 379            23.44761
## 380            28.86667
## 381            38.36772
## 382            32.35843
## 383            32.10148
## 384            34.58290
## 385            32.50530
## 386            47.91453
## 387            42.19430
## 388            32.85552
## 390            44.70858
## 391            39.20399
## 392            29.77279
## 393            36.19858
## 394            35.70202
## 395            35.29730
## 396            25.83688
## 397            27.51263
## 398            34.07421
## 399            36.28783
## 400            26.10801
## 401            31.76104
## 402            29.52803
## 403            34.86158
## 404            31.62533
## 405            26.05474
## 406            31.24540
## 407            43.59258
## 408            49.45883
## 410            30.07084
## 411            29.74758
## 413            24.34772
## 414            33.95405
## 416            39.35209
## 417            39.61137
## 418            44.98515
## 419            41.46987
## 420            38.09897
## 421            33.95113
## 422            47.11730
## 423            45.83043
## 424            43.88010
## 425            34.45027
## 426            45.36287
## 427            27.17653
## 428            29.31177
## 429            25.85097
## 430            31.02555
## 432            32.27077
## 434            34.50555
## 435            35.87369
## 436            35.59795
## 437            33.42805
## 438            48.44532
## 439            33.62187
## 440            45.65262
## 441            25.23907
## 442            30.91330
## 443            44.46743
## 444            27.43738
## 445            40.13415
## 446            44.25930
## 447            37.83687
## 448            38.52092
## 449            34.55414
## 450            28.28300
## 451            37.66720
## 452            43.78714
## 453            43.45600
## 454            30.59248
## 455            27.42535
## 456            36.30357
## 457            32.74787
## 459            26.01837
## 461            36.69341
## 462            26.88142
## 464            39.33805
## 465            39.85845
## 467            39.84752
## 468            38.22722
## 469            34.07565
## 470            23.94667
## 472            37.71247
## 473            38.51919
## 474            31.01496
## 475            32.12325
## 476            27.66158
## 477            37.40268
## 478            35.11708
## 479            41.51106
## 481            40.84805
## 482            46.78790
## 483            45.91149
## 484            49.61072
## 485            36.51288
## 486            27.14262
## 487            46.10083
## 488            26.22212
## 489            36.91947
## 490            32.82987
## 491            40.94590
## 492            39.99572
## 493            39.33639
## 494            26.28574
## 495            28.74918
## 496            25.55477
## 497            41.56032
## 498            28.34777
## 499            37.93134
## 501            51.08272
## 502            43.86273
## 503            42.26945
## 504            32.79800
## 505            32.12519
## 506            29.91053
## 507            45.78978
## 508            32.13103
## 509            33.03715
## 510            39.26602
## 511            37.15952
## 512            37.52531
## 513            39.82142
## 514            37.69905
## 515            46.91393
## 516            25.60736
## 517            29.35595
## 518            34.90010
## 519            41.82301
## 521            37.72036
## 522            30.14928
## 523            38.49192
## 524            37.64800
## 525            38.47860
## 526            33.49317
## 527            30.23520
## 528            41.57004
## 529            30.82337
## 530            35.10083
## 531            27.86447
## 532            39.46228
## 533            37.44082
## 534            36.23658
## 535            38.66695
## 537            41.48363
## 538            37.17015
## 539            43.63497
## 540            34.72457
## 541            34.67185
## 542            31.22399
## 543            46.19802
## 544            47.88790
## 545            37.92504
## 546            47.30453
## 547            39.62676
## 548            35.41253
## 549            36.26660
## 550            33.86576
## 552            34.76413
## 553            41.39128
## 554            29.58200
## 555            39.53728
## 556            44.51937
## 558            31.57915
## 559            39.44488
## 560            44.47138
## 561            41.14230
## 562            43.21562
## 563            33.82382
## 565            41.25516
## 566            40.28137
## 567            37.53697
## 568            39.79487
## 569            34.52063
## 570            38.11275
## 571            39.77878
## 572            37.09758
## 574            37.89808
## 575            43.86272
## 576            26.98457
## 578            37.40604
## 580            29.53265
## 581            27.32400
## 582            27.07536
## 583            28.44703
## 584            36.42407
## 585            30.16867
## 586            40.06047
## 587            25.67740
## 588            30.86990
## 589            46.81098
## 590            36.91382
## 591            27.16763
## 592            28.05980
## 593            40.70735
## 595            32.11105
## 596            30.88382
## 597            29.21595
## 598            29.27796
## 599            31.47782
## 600            29.22693
## 602            33.31109
## 603            35.95182
## 604            30.73700
## 605            41.62548
## 606            47.58509
## 607            28.97820
## 608            29.36523
## 609            29.61637
## 610            28.96045
## 611            28.79898
## 613            29.81638
## 614            26.02641
## 615            28.50090
## 616            32.45817
## 617            28.28448
## 618            27.35253
## 619            46.65899
## 620            43.14780
## 621            29.07459
## 622            28.93938
## 623            36.18645
## 624            29.74168
## 625            28.82398
## 626            28.31362
## 627            31.15977
## 628            30.09557
## 629            30.95017
## 630            28.17202
## 631            30.39811
## 632            29.94238
## 633            24.69690
## 634            29.95090
## 635            27.27866
## 636            32.85821
## 637            29.09339
## 639            29.68021
## 640            31.99721
## 641            39.82566
## 643            46.95691
## 644            36.47249
## 645            44.98860
## 648            41.14533
## 649            45.91713
## 650            39.90497
## 651            49.41028
## 652            46.12992
## 653            44.14057
## 654            40.01273
## 655            46.25890
## 656            28.63617
## 657            29.07410
## 658            25.73931
## 659            38.36240
## 660            43.98823
## 661            35.89332
## 662            29.15824
## 663            30.48737
## 664            30.64823
## 666            30.65805
## 667            29.38988
## 668            28.86433
## 669            29.20572
## 670            29.16825
## 671            27.41727
## 672            47.85414
## 673            45.23559
## 674            45.85387
## 675            51.77945
## 676            33.58796
## 677            47.14893
## 678            48.61420
## 680            47.02733
## 681            45.27297
## 682            44.29821
## 683            42.04925
## 684            46.78817
## 685            41.00230
## 686            48.72863
## 687            42.65752
## 688            46.67601
## 689            49.69087
## 690            44.97548
## 691            33.67652
## 692            46.76098
## 693            49.13465
## 694            46.70185
## 695            41.09273
## 696            44.45594
## 697            40.27366
## 698            41.06512
## 699            49.01633
## 700            44.52923
## 701            41.72809
## 702            51.04920
## 703            49.26728
## 704            44.71859
## 705            47.35832
## 706            42.29107
## 708            48.26730
## 709            43.84415
## 711            48.34129
## 712            47.39600
## 713            44.34830
## 715            43.21166
## 716            45.77719
## 718            41.92215
## 719            49.61175
## 720            44.56448
## 721            49.60035
## 722            39.30251
## 723            34.46848
## 725            31.60887
## 726            37.12275
## 727            44.87564
## 729            45.15552
## 730            39.54505
## 732            47.84007
## 733            39.41730
## 734            43.98038
## 735            42.68342
## 736            43.32003
## 737            46.78693
## 738            47.51233
## 739            47.96315
## 740            44.33135
## 741            50.60500
## 742            37.91215
## 743            45.77058
## 744            45.22809
## 746            45.36667
## 748            48.74633
## 750            39.27418
## 751            48.68549
## 752            46.42552
## 753            44.56010
## 754            47.24523
## 755            49.35128
## 756            42.57146
## 757            44.47908
## 758            46.43523
## 759            43.36737
## 760            45.05604
## 761            49.37388
## 762            46.08283
## 763            48.44553
## 764            38.35835
## 765            50.56053
## 766            48.94945
## 767            50.35841
## 768            44.52297
## 769            50.72714
## 770            32.29154
## 771            39.80217
## 772            42.00310
## 773            46.62385
## 774            45.74840
## 775            43.58075
## 776            38.48047
## 777            45.69206
## 779            45.15127
## 780            47.54275
## 781            41.88547
## 782            47.48400
## 783            45.16894
## 784            44.35898
## 786            37.86033
## 788            40.39038
## 789            45.80155
## 790            42.02975
## 792            45.18836
## 793            52.22173
## 795            35.48338
## 796            40.20499
## 797            45.32695
## 798            46.07027
## 799            45.05012
## 800            48.83575
## 801            48.22000
## 802            48.74843
## 803            46.03181
## 805            46.90022
## 806            35.24142
## 807            48.41335
## 808            42.75508
## 809            47.93292
## 810            46.66600
## 811            39.25310
## 812            38.91882
## 813            45.65098
## 814            45.47829
## 815            44.91792
## 816            40.67470
## 817            43.48048
## 818            42.48980
## 819            50.93312
## 820            36.22197
## 821            47.08392
## 822            42.03410
## 823            48.69161
## 824            45.92235
## 825            47.71638
## 826            41.74062
## 827            49.59363
## 828            45.73362
## 830            46.72648
## 832            43.36620
## 833            49.50017
## 835            46.98187
## 836            46.93607
## 837            48.25977
## 838            38.29290
## 839            52.10153
## 840            48.24355
## 841            45.33510
## 842            48.11852
## 844            45.02563
## 845            45.00008
## 846            48.80027
## 847            46.98942
## 849            43.58438
## 850            37.28142
## 851            47.78715
## 852            47.12493
## 853            47.06663
## 854            46.80414
## 856            47.10178
## 857            46.04382
## 859            47.26899
## 861            46.82807
## 862            48.06422
## 863            44.54758
## 864            36.35768
## 865            43.45988
## 866            36.01937
## 867            38.68974
## 869            43.19138
## 870            46.69940
## 871            33.17693
## 872            47.82498
## 873            44.16850
## 874            38.58100
## 875            42.68057
## 877            48.48238
## 878            46.99828
## 879            46.85743
## 880            38.44077
## 882            46.43560
## 883            47.00482
## 884            49.02682
## 885            41.28668
## 886            47.49728
## 887            48.47856
## 888            45.17052
## 889            49.14512
## 890            43.79313
## 891            41.37634
## 892            43.83520
## 893            40.17075
## 894            46.56880
## 895            42.59287
## 896            46.27906
## 897            50.68408
## 898            44.86977
## 899            48.51020
## 900            34.82052
## 901            47.33959
## 902            48.74215
## 903            44.72132
## 904            49.58649
## 905            39.07799
## 906            45.84705
## 907            36.50270
## 908            47.03588
## 909            44.85560
## 910            45.33803
## 911            46.71995
## 912            47.86710
## 913            41.88120
## 914            46.50531
## 915            46.70597
## 916            48.37718
## 917            42.66797
## 918            48.00157
## 919            45.59858
## 920            46.38635
## 921            43.41797
## 922            51.58504
## 923            48.07688
## 924            44.27410
## 925            37.23202
## 926            48.73507
## 927            48.08388
## 928            44.73363
## 929            48.96107
## 930            44.58848
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## 110680         45.54710
## 110681         47.40666
## 110683         47.24668
## 110684         48.05502
## 110685         50.46107
## 110687         47.00058
## 110688         49.91717
## 110689         43.83100
## 110691         49.21955
## 110692         48.44791
## 110693         30.73817
## 110694         39.91030
## 110696         51.36498
## 110699         49.90070
## 110700         47.96427
## 110701         47.73607
## 110702         50.39362
## 110703         46.61277
## 110704         44.87789
## 110706         50.55840
## 110707         45.33662
## 110708         50.82434
## 110709         47.07294
## 110710         51.02887
## 110712         44.90323
## 110713         50.82233
## 110714         35.00792
## 110715         51.11683
## 110716         46.10210
## 110717         48.60042
## 110719         43.82833
## 110720         43.57241
## 110721         48.44560
## 110722         48.03889
## 110723         50.82253
## 110724         47.44712
## 110725         50.62296
## 110726         48.86000
## 110727         48.70242
## 110730         43.88245
## 110731         47.88207
## 110733         42.79768
## 110734         44.77060
## 110735         46.65448
## 110736         44.01052
## 110737         46.57368
## 110738         46.93443
## 110739         50.40463
## 110740         43.28262
## 110741         44.72255
## 110742         50.12262
## 110744         48.55802
## 110745         50.86620
## 110746         53.29292
## 110747         46.16477
## 110748         45.15757
## 110749         52.57787
## 110750         44.00394
## 110751         49.46618
## 110752         49.25591
## 110753         47.87844
## 110754         46.92490
## 110755         49.19356
## 110756         50.21175
## 110757         50.23163
## 110758         50.69952
## 110759         47.09611
## 110760         40.63877
## 110761         47.25122
## 110762         45.62077
## 110763         44.45205
## 110764         44.42840
## 110765         45.00426
## 110766         50.41205
## 110767         49.38726
## 110769         46.28257
## 110770         45.32638
## 110771         51.51185
## 110772         46.10078
## 110773         35.76558
## 110774         43.14302
## 110775         40.57043
## 110776         44.00411
## 110777         52.12478
## 110778         45.58487
## 110779         46.54713
## 110780         47.04545
## 110781         48.59273
## 110782         48.98599
## 110783         45.45122
## 110784         49.93819
## 110785         51.59408
## 110786         45.91108
## 110787         42.12703
## 110788         49.20132
## 110790         45.98720
## 110791         50.43388
## 110792         50.29508
## 110793         44.05100
## 110794         43.99263
## 110797         48.25693
## 110798         45.01532
## 110799         47.28697
## 110800         49.63142
## 110801         43.70960
## 110802         44.38852
## 110803         51.80657
## 110804         47.27715
## 110805         47.24455
## 110806         50.09499
## 110807         44.53616
## 110809         49.65210
## 110810         35.96728
## 110811         49.30212
## 110813         48.51188
## 110814         43.03483
## 110815         45.07537
## 110816         51.57806
## 110817         44.38363
## 110819         51.57353
## 110820         41.58525
## 110821         47.31270
## 110822         49.17785
## 110823         46.46840
## 110825         42.78372
## 110827         49.78435
## 110828         48.00418
## 110829         52.19120
## 110830         48.36543
## 110832         49.61793
## 110833         42.81363
## 110834         47.97805
## 110835         43.49028
## 110836         42.83740
## 110837         46.97654
## 110838         50.20883
## 110839         45.78477
## 110841         50.93097
## 110842         49.23112
## 110843         43.77212
## 110844         51.66728
## 110845         46.93225
## 110846         50.98523
## 110847         47.59824
## 110848         46.35848
## 110849         52.07465
## 110850         51.48438
## 110851         44.89973
## 110852         50.40877
## 110853         48.47747
## 110854         42.38644
## 110855         49.54533
## 110857         51.90297
## 110858         49.14185
## 110859         47.31925
## 110860         46.33565
## 110861         48.49223
## 110862         39.22171
## 110864         50.22015
## 110865         42.89041
## 110866         48.42858
## 110867         50.59920
## 110868         48.13970
## 110869         47.82001
## 110870         45.04300
## 110871         42.53905
## 110874         48.59530
## 110875         51.85247
## 110876         44.53648
## 110877         44.65903
## 110878         50.28807
## 110879         52.17793
## 110880         39.24278
## 110881         43.55107
## 110882         47.80860
## 110883         43.30002
## 110884         46.07338
## 110885         49.15578
## 110886         48.53688
## 110887         45.08220
## 110888         45.05120
## 110889         48.83277
## 110890         50.69828
## 110893         29.32503
## 110894         47.35750
## 110895         43.97000
## 110896         50.35292
## 110897         49.32548
## 110898         46.30717
## 110899         49.26170
## 110900         47.74220
## 110901         43.46492
## 110902         44.58697
## 110903         47.00302
## 110904         49.64078
## 110905         45.74945
## 110906         51.18610
## 110907         50.71837
## 110908         46.58815
## 110909         47.45290
## 110910         50.87450
## 110911         48.20402
## 110912         48.62643
## 110913         35.63082
## 110914         34.16935
## 110915         49.74449
## 110916         49.80103
## 110917         48.90701
## 110918         47.53560
## 110919         48.92532
## 110921         42.95281
## 110922         41.60523
## 110923         43.58320
## 110924         48.64151
## 110925         45.75542
## 110926         42.47897
## 110927         50.68520
## 110928         49.56453
## 110929         47.12246
## 110930         48.24753
## 110931         43.29351
## 110932         49.44413
## 110933         42.80473
## 110934         44.98397
## 110935         48.23627
## 110936         49.09605
## 110937         47.16143
## 110938         48.89758
## 110939         47.67297
## 110940         48.73798
## 110941         47.16567
## 110942         47.68230
## 110943         47.81443
## 110945         48.24905
## 110946         52.53285
## 110947         49.49112
## 110948         47.47953
## 110949         46.34631
## 110950         50.78353
## 110951         49.80868
## 110952         50.73889
## 110953         41.79662
## 110955         41.92207
## 110956         46.96205
## 110957         48.60794
## 110958         46.57693
## 110959         48.11273
## 110960         45.06902
## 110961         49.11560
## 110962         46.33388
## 110963         47.00392
## 110964         50.72317
## 110966         49.93758
## 110967         46.94523
## 110968         48.41300
## 110969         45.04331
## 110971         49.89469
## 110972         49.26660
##  [ reached 'max' / getOption("max.print") -- omitted 109454 rows ]

Take a look at the variable importance measures

# The "importance" argument provides a table that includes the importance
# of each variable to the accuracy of the classification.
as.data.frame(varImp(pop_RF, type = 2, scale = TRUE)) #type 1 is error on oob, 
##                    Overall
## acousticness     3841.0445
## danceability     2250.1343
## duration_ms      2993.5943
## energy           2658.1052
## instrumentalness 1599.8494
## key              3672.9501
## liveness         2068.6330
## loudness         3687.1308
## mode              200.6078
## speechiness      2003.7502
## tempo            1661.8719
## time_signature    377.4922
## valence          2046.0900
                                                                      # type 2 is total decrease
# in node impurity as measured by the Gini index, look at the differences, stop by wine for example. 
                                                        # scale divides the measures by 
                                                        # their standard errors

Using the training data sets to tune the model in consideration of the number of trees, the number of variables to sample and the sample size that optimize the model output.

#### Optimize the random forest model ####

# Let's just say we want to do the best we can to label pregnant customers as pregnant
# later we can certainly adjust the threshold but want to tune to optimize the models ability 
# to identify the positive target class. 

set.seed(1984)  
pop_RF_2 = randomForest(as.numeric(popularity)~.,          #<- formula, response variable ~ predictors.
                              #   the period means 'use all other variables in the data'.
                              pop_train,     #<- A data frame with variables to be used.
                              #y = NULL,           #<- A response vector. This is unnecessary because we're specifying a response formula.
                              #subset = NULL,      #<- This is unneccessary because we're using all the rows in the training data set.
                              #xtest = NULL,       #<- This is already defined in the formula by the ".".
                              #ytest = NULL,       #<- This is already defined in the formula by "PREGNANT".
                              ntree = 1000,          #<- Number of trees to grow. This should not be set to too small a number, to ensure that every input row gets classified at least a few times.
                              mtry = 5,            #<- Number of variables randomly sampled as candidates at each split. Default number for classification is sqrt(# of variables). Default number for regression is (# of variables / 3).
                              replace = TRUE,      #<- Should sampled data points be replaced.
                              #classwt = NULL,     #<- Priors of the classes. We will work through this later. 
                              #strata = NULL,      #<- Not necessary for our purpose here.
                              sampsize = 10000,      #<- Size of sample to draw each time.
                              nodesize = 5,        #<- Minimum numbers of data points in terminal nodes.
                              #maxnodes = NULL,    #<- The "nodesize" argument limits the number of maximum splits. 
                              importance = TRUE,   #<- Should importance predictors be assessed?
                              #localImp = FALSE,   #<- Should casewise importance measure be computed? (Setting this to TRUE will override importance.)
                              proximity = FALSE,    #<- Should a proximity measure between rows be calculated?
                              norm.votes = TRUE,   #<- If TRUE (default), the final result of votes are expressed as fractions. If FALSE, raw vote counts are returned (useful for combining results from different runs).
                              do.trace = TRUE,     #<- If set to TRUE, give a more verbose output as randomForest is run.
                              keep.forest = TRUE,  #<- If set to FALSE, the forest will not be retained in the output object. If xtest is given, defaults to FALSE.
                              keep.inbag = TRUE) 
##      |      Out-of-bag   |
## Tree |      MSE  %Var(y) |
##    1 |    402.1   121.45 |
##    2 |    310.8    93.87 |
##    3 |    272.2    82.22 |
##    4 |    253.2    76.47 |
##    5 |    242.3    73.17 |
##    6 |    234.9    70.96 |
##    7 |    229.8    69.40 |
##    8 |    225.4    68.08 |
##    9 |    222.6    67.23 |
##   10 |    220.2    66.51 |
##   11 |    218.2    65.91 |
##   12 |    216.4    65.37 |
##   13 |    215.1    64.97 |
##   14 |    213.9    64.60 |
##   15 |    212.9    64.31 |
##   16 |    212.2    64.08 |
##   17 |    211.3    63.83 |
##   18 |    210.6    63.60 |
##   19 |    209.9    63.40 |
##   20 |    209.4    63.24 |
##   21 |    208.8    63.06 |
##   22 |    208.3    62.93 |
##   23 |      208    62.82 |
##   24 |    207.6    62.71 |
##   25 |    207.3    62.60 |
##   26 |    206.9    62.50 |
##   27 |    206.6    62.41 |
##   28 |    206.3    62.32 |
##   29 |    206.1    62.24 |
##   30 |    205.7    62.15 |
##   31 |    205.5    62.06 |
##   32 |    205.2    61.98 |
##   33 |    205.1    61.95 |
##   34 |      205    61.91 |
##   35 |    204.9    61.88 |
##   36 |    204.7    61.83 |
##   37 |    204.5    61.78 |
##   38 |    204.4    61.75 |
##   39 |    204.3    61.71 |
##   40 |    204.2    61.67 |
##   41 |      204    61.63 |
##   42 |    203.8    61.57 |
##   43 |    203.7    61.53 |
##   44 |    203.6    61.51 |
##   45 |    203.5    61.48 |
##   46 |    203.4    61.44 |
##   47 |    203.3    61.40 |
##   48 |    203.2    61.38 |
##   49 |    203.1    61.36 |
##   50 |    203.1    61.34 |
##   51 |      203    61.32 |
##   52 |    202.9    61.29 |
##   53 |    202.9    61.27 |
##   54 |    202.8    61.26 |
##   55 |    202.7    61.24 |
##   56 |    202.7    61.21 |
##   57 |    202.6    61.20 |
##   58 |    202.6    61.19 |
##   59 |    202.5    61.17 |
##   60 |    202.5    61.16 |
##   61 |    202.4    61.15 |
##   62 |    202.4    61.12 |
##   63 |    202.3    61.11 |
##   64 |    202.3    61.10 |
##   65 |    202.2    61.07 |
##   66 |    202.1    61.05 |
##   67 |    202.1    61.05 |
##   68 |    202.1    61.04 |
##   69 |      202    61.03 |
##   70 |      202    61.01 |
##   71 |    201.9    61.00 |
##   72 |    201.9    60.98 |
##   73 |    201.8    60.96 |
##   74 |    201.8    60.95 |
##   75 |    201.7    60.94 |
##   76 |    201.7    60.93 |
##   77 |    201.7    60.91 |
##   78 |    201.6    60.90 |
##   79 |    201.6    60.89 |
##   80 |    201.5    60.88 |
##   81 |    201.5    60.87 |
##   82 |    201.5    60.86 |
##   83 |    201.4    60.84 |
##   84 |    201.4    60.83 |
##   85 |    201.4    60.82 |
##   86 |    201.3    60.81 |
##   87 |    201.3    60.80 |
##   88 |    201.3    60.79 |
##   89 |    201.2    60.78 |
##   90 |    201.2    60.77 |
##   91 |    201.2    60.76 |
##   92 |    201.1    60.74 |
##   93 |    201.1    60.74 |
##   94 |      201    60.72 |
##   95 |      201    60.72 |
##   96 |      201    60.71 |
##   97 |      201    60.71 |
##   98 |      201    60.71 |
##   99 |      201    60.70 |
##  100 |    200.9    60.69 |
##  101 |    200.9    60.68 |
##  102 |    200.9    60.67 |
##  103 |    200.9    60.67 |
##  104 |    200.8    60.66 |
##  105 |    200.8    60.66 |
##  106 |    200.8    60.66 |
##  107 |    200.8    60.64 |
##  108 |    200.8    60.65 |
##  109 |    200.8    60.65 |
##  110 |    200.8    60.64 |
##  111 |    200.8    60.64 |
##  112 |    200.7    60.63 |
##  113 |    200.7    60.63 |
##  114 |    200.7    60.63 |
##  115 |    200.7    60.63 |
##  116 |    200.7    60.63 |
##  117 |    200.7    60.62 |
##  118 |    200.7    60.62 |
##  119 |    200.7    60.61 |
##  120 |    200.7    60.61 |
##  121 |    200.6    60.60 |
##  122 |    200.6    60.60 |
##  123 |    200.6    60.59 |
##  124 |    200.6    60.59 |
##  125 |    200.6    60.59 |
##  126 |    200.6    60.60 |
##  127 |    200.6    60.60 |
##  128 |    200.6    60.60 |
##  129 |    200.6    60.59 |
##  130 |    200.6    60.59 |
##  131 |    200.6    60.59 |
##  132 |    200.6    60.59 |
##  133 |    200.6    60.58 |
##  134 |    200.6    60.58 |
##  135 |    200.5    60.57 |
##  136 |    200.5    60.57 |
##  137 |    200.5    60.57 |
##  138 |    200.5    60.56 |
##  139 |    200.5    60.56 |
##  140 |    200.5    60.56 |
##  141 |    200.5    60.55 |
##  142 |    200.5    60.55 |
##  143 |    200.5    60.55 |
##  144 |    200.5    60.56 |
##  145 |    200.5    60.55 |
##  146 |    200.5    60.55 |
##  147 |    200.4    60.55 |
##  148 |    200.5    60.55 |
##  149 |    200.4    60.55 |
##  150 |    200.5    60.55 |
##  151 |    200.4    60.54 |
##  152 |    200.4    60.53 |
##  153 |    200.4    60.53 |
##  154 |    200.4    60.53 |
##  155 |    200.4    60.52 |
##  156 |    200.4    60.52 |
##  157 |    200.4    60.52 |
##  158 |    200.4    60.52 |
##  159 |    200.4    60.52 |
##  160 |    200.3    60.51 |
##  161 |    200.3    60.51 |
##  162 |    200.3    60.51 |
##  163 |    200.3    60.51 |
##  164 |    200.3    60.51 |
##  165 |    200.3    60.50 |
##  166 |    200.3    60.50 |
##  167 |    200.3    60.50 |
##  168 |    200.3    60.50 |
##  169 |    200.3    60.50 |
##  170 |    200.3    60.50 |
##  171 |    200.3    60.49 |
##  172 |    200.3    60.49 |
##  173 |    200.3    60.49 |
##  174 |    200.3    60.49 |
##  175 |    200.2    60.48 |
##  176 |    200.2    60.48 |
##  177 |    200.2    60.48 |
##  178 |    200.2    60.47 |
##  179 |    200.2    60.47 |
##  180 |    200.2    60.48 |
##  181 |    200.2    60.48 |
##  182 |    200.2    60.48 |
##  183 |    200.2    60.47 |
##  184 |    200.2    60.47 |
##  185 |    200.2    60.47 |
##  186 |    200.2    60.46 |
##  187 |    200.2    60.46 |
##  188 |    200.2    60.46 |
##  189 |    200.2    60.46 |
##  190 |    200.2    60.46 |
##  191 |    200.2    60.46 |
##  192 |    200.2    60.46 |
##  193 |    200.1    60.45 |
##  194 |    200.1    60.45 |
##  195 |    200.1    60.45 |
##  196 |    200.1    60.45 |
##  197 |    200.1    60.45 |
##  198 |    200.1    60.45 |
##  199 |    200.1    60.45 |
##  200 |    200.1    60.44 |
##  201 |    200.1    60.44 |
##  202 |    200.1    60.44 |
##  203 |    200.1    60.44 |
##  204 |    200.1    60.44 |
##  205 |    200.1    60.44 |
##  206 |    200.1    60.44 |
##  207 |    200.1    60.43 |
##  208 |    200.1    60.43 |
##  209 |    200.1    60.43 |
##  210 |      200    60.42 |
##  211 |      200    60.42 |
##  212 |      200    60.42 |
##  213 |      200    60.42 |
##  214 |      200    60.42 |
##  215 |      200    60.42 |
##  216 |      200    60.42 |
##  217 |      200    60.42 |
##  218 |      200    60.42 |
##  219 |      200    60.42 |
##  220 |      200    60.42 |
##  221 |      200    60.42 |
##  222 |      200    60.41 |
##  223 |      200    60.41 |
##  224 |      200    60.41 |
##  225 |      200    60.41 |
##  226 |      200    60.40 |
##  227 |      200    60.41 |
##  228 |      200    60.41 |
##  229 |      200    60.40 |
##  230 |      200    60.40 |
##  231 |      200    60.40 |
##  232 |      200    60.40 |
##  233 |    199.9    60.39 |
##  234 |    199.9    60.39 |
##  235 |    199.9    60.39 |
##  236 |    199.9    60.39 |
##  237 |    199.9    60.38 |
##  238 |    199.9    60.38 |
##  239 |    199.9    60.38 |
##  240 |    199.9    60.38 |
##  241 |    199.9    60.38 |
##  242 |    199.9    60.37 |
##  243 |    199.9    60.37 |
##  244 |    199.9    60.37 |
##  245 |    199.9    60.37 |
##  246 |    199.9    60.37 |
##  247 |    199.9    60.37 |
##  248 |    199.9    60.37 |
##  249 |    199.9    60.37 |
##  250 |    199.9    60.37 |
##  251 |    199.9    60.37 |
##  252 |    199.9    60.37 |
##  253 |    199.9    60.37 |
##  254 |    199.9    60.37 |
##  255 |    199.9    60.37 |
##  256 |    199.9    60.37 |
##  257 |    199.9    60.37 |
##  258 |    199.9    60.37 |
##  259 |    199.9    60.37 |
##  260 |    199.9    60.37 |
##  261 |    199.9    60.37 |
##  262 |    199.9    60.37 |
##  263 |    199.9    60.37 |
##  264 |    199.9    60.37 |
##  265 |    199.9    60.37 |
##  266 |    199.9    60.37 |
##  267 |    199.9    60.37 |
##  268 |    199.9    60.37 |
##  269 |    199.9    60.37 |
##  270 |    199.9    60.37 |
##  271 |    199.8    60.36 |
##  272 |    199.8    60.36 |
##  273 |    199.8    60.36 |
##  274 |    199.8    60.36 |
##  275 |    199.8    60.36 |
##  276 |    199.8    60.36 |
##  277 |    199.8    60.36 |
##  278 |    199.8    60.36 |
##  279 |    199.8    60.36 |
##  280 |    199.8    60.36 |
##  281 |    199.8    60.35 |
##  282 |    199.8    60.35 |
##  283 |    199.8    60.35 |
##  284 |    199.8    60.35 |
##  285 |    199.8    60.35 |
##  286 |    199.8    60.35 |
##  287 |    199.8    60.35 |
##  288 |    199.8    60.35 |
##  289 |    199.8    60.35 |
##  290 |    199.8    60.35 |
##  291 |    199.8    60.35 |
##  292 |    199.8    60.35 |
##  293 |    199.8    60.35 |
##  294 |    199.8    60.35 |
##  295 |    199.8    60.35 |
##  296 |    199.8    60.35 |
##  297 |    199.8    60.35 |
##  298 |    199.8    60.35 |
##  299 |    199.8    60.35 |
##  300 |    199.8    60.35 |
##  301 |    199.8    60.35 |
##  302 |    199.8    60.35 |
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##  841 |    199.3    60.21 |
##  842 |    199.3    60.21 |
##  843 |    199.3    60.21 |
##  844 |    199.3    60.21 |
##  845 |    199.3    60.21 |
##  846 |    199.3    60.21 |
##  847 |    199.3    60.21 |
##  848 |    199.3    60.21 |
##  849 |    199.3    60.21 |
##  850 |    199.3    60.21 |
##  851 |    199.3    60.21 |
##  852 |    199.3    60.21 |
##  853 |    199.3    60.21 |
##  854 |    199.3    60.21 |
##  855 |    199.3    60.21 |
##  856 |    199.3    60.21 |
##  857 |    199.3    60.21 |
##  858 |    199.3    60.21 |
##  859 |    199.3    60.21 |
##  860 |    199.3    60.21 |
##  861 |    199.3    60.21 |
##  862 |    199.3    60.21 |
##  863 |    199.3    60.21 |
##  864 |    199.3    60.21 |
##  865 |    199.3    60.21 |
##  866 |    199.3    60.21 |
##  867 |    199.3    60.21 |
##  868 |    199.3    60.21 |
##  869 |    199.3    60.21 |
##  870 |    199.3    60.21 |
##  871 |    199.3    60.21 |
##  872 |    199.3    60.21 |
##  873 |    199.3    60.21 |
##  874 |    199.3    60.21 |
##  875 |    199.3    60.21 |
##  876 |    199.3    60.21 |
##  877 |    199.3    60.21 |
##  878 |    199.3    60.21 |
##  879 |    199.3    60.21 |
##  880 |    199.3    60.21 |
##  881 |    199.3    60.20 |
##  882 |    199.3    60.20 |
##  883 |    199.3    60.20 |
##  884 |    199.3    60.20 |
##  885 |    199.3    60.20 |
##  886 |    199.3    60.20 |
##  887 |    199.3    60.20 |
##  888 |    199.3    60.20 |
##  889 |    199.3    60.20 |
##  890 |    199.3    60.20 |
##  891 |    199.3    60.20 |
##  892 |    199.3    60.20 |
##  893 |    199.3    60.20 |
##  894 |    199.3    60.20 |
##  895 |    199.3    60.20 |
##  896 |    199.3    60.20 |
##  897 |    199.3    60.20 |
##  898 |    199.3    60.20 |
##  899 |    199.3    60.20 |
##  900 |    199.3    60.20 |
##  901 |    199.3    60.20 |
##  902 |    199.3    60.20 |
##  903 |    199.3    60.20 |
##  904 |    199.3    60.20 |
##  905 |    199.3    60.20 |
##  906 |    199.3    60.20 |
##  907 |    199.3    60.20 |
##  908 |    199.3    60.20 |
##  909 |    199.3    60.20 |
##  910 |    199.3    60.20 |
##  911 |    199.3    60.20 |
##  912 |    199.3    60.20 |
##  913 |    199.3    60.20 |
##  914 |    199.3    60.20 |
##  915 |    199.3    60.20 |
##  916 |    199.3    60.20 |
##  917 |    199.3    60.20 |
##  918 |    199.3    60.20 |
##  919 |    199.3    60.20 |
##  920 |    199.3    60.20 |
##  921 |    199.3    60.20 |
##  922 |    199.3    60.20 |
##  923 |    199.3    60.20 |
##  924 |    199.3    60.20 |
##  925 |    199.3    60.20 |
##  926 |    199.3    60.20 |
##  927 |    199.3    60.20 |
##  928 |    199.3    60.20 |
##  929 |    199.3    60.20 |
##  930 |    199.3    60.20 |
##  931 |    199.3    60.20 |
##  932 |    199.3    60.20 |
##  933 |    199.3    60.20 |
##  934 |    199.3    60.20 |
##  935 |    199.3    60.20 |
##  936 |    199.3    60.20 |
##  937 |    199.3    60.20 |
##  938 |    199.3    60.20 |
##  939 |    199.3    60.20 |
##  940 |    199.3    60.20 |
##  941 |    199.3    60.19 |
##  942 |    199.3    60.19 |
##  943 |    199.3    60.19 |
##  944 |    199.3    60.20 |
##  945 |    199.3    60.20 |
##  946 |    199.3    60.20 |
##  947 |    199.3    60.20 |
##  948 |    199.3    60.20 |
##  949 |    199.3    60.20 |
##  950 |    199.3    60.20 |
##  951 |    199.3    60.20 |
##  952 |    199.3    60.20 |
##  953 |    199.3    60.20 |
##  954 |    199.3    60.20 |
##  955 |    199.3    60.19 |
##  956 |    199.3    60.19 |
##  957 |    199.3    60.19 |
##  958 |    199.3    60.20 |
##  959 |    199.3    60.20 |
##  960 |    199.3    60.19 |
##  961 |    199.3    60.19 |
##  962 |    199.3    60.19 |
##  963 |    199.3    60.19 |
##  964 |    199.3    60.19 |
##  965 |    199.3    60.19 |
##  966 |    199.3    60.19 |
##  967 |    199.3    60.19 |
##  968 |    199.3    60.19 |
##  969 |    199.3    60.19 |
##  970 |    199.3    60.19 |
##  971 |    199.3    60.19 |
##  972 |    199.3    60.19 |
##  973 |    199.3    60.19 |
##  974 |    199.3    60.19 |
##  975 |    199.3    60.19 |
##  976 |    199.3    60.19 |
##  977 |    199.3    60.19 |
##  978 |    199.3    60.19 |
##  979 |    199.3    60.19 |
##  980 |    199.3    60.19 |
##  981 |    199.3    60.19 |
##  982 |    199.3    60.19 |
##  983 |    199.3    60.19 |
##  984 |    199.3    60.19 |
##  985 |    199.3    60.19 |
##  986 |    199.3    60.19 |
##  987 |    199.3    60.19 |
##  988 |    199.3    60.19 |
##  989 |    199.3    60.19 |
##  990 |    199.3    60.19 |
##  991 |    199.3    60.19 |
##  992 |    199.3    60.19 |
##  993 |    199.3    60.19 |
##  994 |    199.3    60.19 |
##  995 |    199.3    60.19 |
##  996 |    199.3    60.19 |
##  997 |    199.3    60.19 |
##  998 |    199.3    60.19 |
##  999 |    199.3    60.19 |
## 1000 |    199.3    60.19 |
sqrt(pop_RF$mse[length(pop_RF$mse)])
## [1] 15.4595
sqrt(pop_RF_2$mse[length(pop_RF_2$mse)])
## [1] 14.11607
as.data.frame(pop_RF_2$predicted)
##        pop_RF_2$predicted
## 1               29.562636
## 2               41.986970
## 3               36.657178
## 4               37.171954
## 5               17.821990
## 6               34.073954
## 7               26.336143
## 8               43.992757
## 9               46.021827
## 10              40.627561
## 11              26.031230
## 12              30.421872
## 13              50.611717
## 14              29.324852
## 15              27.719571
## 16              20.160792
## 17              19.694223
## 18              38.017852
## 19              47.466176
## 20              47.123416
## 21              44.189251
## 22              36.732725
## 23              36.776409
## 24              17.420942
## 25              50.411665
## 26              14.482829
## 27              48.462165
## 28              32.450069
## 29              19.393302
## 30              39.553641
## 31              43.449651
## 32              20.429503
## 33              22.562526
## 34              21.503323
## 35              39.077391
## 36              30.342907
## 37              48.294089
## 38              40.683665
## 39              27.587106
## 40              27.400581
## 42              26.447303
## 43              24.436362
## 44              32.952795
## 45              30.955016
## 46              28.500070
## 47              44.431206
## 49              35.617016
## 50              29.815444
## 51              31.079635
## 52              29.187675
## 53              23.348168
## 54              41.117640
## 55              15.143462
## 56              23.248483
## 57              24.333509
## 58              27.384576
## 59              27.126496
## 61              22.121128
## 63              23.955150
## 64              34.805051
## 65              36.928669
## 66              40.342411
## 68              27.590928
## 69              22.504031
## 70              30.928229
## 71              13.701252
## 72              35.043452
## 73              18.120384
## 74              26.800406
## 75              16.211326
## 77              25.826930
## 78              36.635597
## 80              19.089968
## 81              46.557362
## 82              21.825413
## 83              17.663466
## 84              28.018051
## 85              32.486316
## 86              29.405130
## 87              34.277190
## 88              38.197517
## 89              39.253588
## 90              46.130652
## 92              40.273249
## 93              48.596321
## 94              23.861955
## 95              37.868415
## 96              38.790644
## 97              28.368211
## 99              27.501316
## 100             54.472159
## 101             40.061935
## 102             16.818770
## 103             15.567677
## 104             46.819535
## 105             21.496792
## 106             35.207773
## 107             37.090548
## 108             46.132565
## 109             35.636484
## 110             38.669450
## 111             41.242795
## 112             39.560021
## 113             41.320355
## 114             25.987474
## 116             34.789727
## 117             50.333386
## 118             31.695291
## 119             48.052866
## 120             18.138523
## 121             28.537904
## 122             23.590988
## 123             32.472269
## 124             35.687354
## 125             45.303688
## 126             19.272414
## 127             35.605613
## 128             45.824302
## 129             28.231359
## 130             33.235935
## 131             23.817889
## 132             37.885525
## 133             29.380032
## 134             26.204455
## 135             50.082192
## 136             49.267918
## 137             55.812261
## 138             58.173459
## 140             55.106978
## 141             49.712037
## 142             48.150451
## 143             37.642115
## 144             43.479402
## 145             44.708325
## 146             46.489396
## 147             52.501755
## 148             59.878819
## 149             55.647873
## 150             53.360589
## 152             48.428114
## 153             56.960000
## 154             50.888627
## 155             54.340756
## 156             49.778333
## 157             58.164410
## 158             55.081462
## 159             40.318888
## 160             49.715941
## 161             51.415611
## 162             50.681546
## 163             47.993415
## 164             46.065323
## 165             50.531807
## 166             55.057027
## 167             51.374209
## 168             51.461801
## 169             57.510112
## 170             54.108010
## 171             50.945338
## 173             53.640385
## 174             46.408014
## 176             55.336985
## 177             50.515566
## 178             51.075745
## 179             47.131566
## 180             39.406405
## 181             49.334475
## 182             51.435769
## 183             49.184839
## 184             54.619651
## 185             52.824181
## 186             50.521874
## 187             53.681847
## 188             48.144259
## 189             54.525148
## 190             50.475640
## 191             50.800905
## 192             46.243365
## 193             53.248878
## 194             56.187223
## 195             54.489965
## 196             51.665635
## 197             46.631141
## 198             51.411434
## 199             45.549231
## 203             51.343467
## 204             57.122094
## 205             55.836723
## 206             53.639892
## 207             53.963010
## 208             53.648361
## 209             50.023413
## 210             54.660462
## 211             45.488580
## 212             55.695890
## 213             45.290101
## 214             49.751334
## 215             58.072222
## 216             44.972408
## 217             57.109895
## 218             46.446757
## 219             57.563630
## 220             41.430344
## 221             60.351776
## 222             54.292040
## 223             45.961264
## 224             53.949913
## 225             49.176206
## 226             52.438027
## 227             49.414974
## 228             54.793045
## 229             49.218145
## 230             59.525088
## 231             56.058527
## 232             50.764636
## 233             57.181799
## 235             44.091763
## 236             47.697718
## 237             42.554717
## 238             49.945445
## 239             46.462776
## 241             56.224850
## 242             54.381088
## 244             46.889312
## 245             55.194874
## 246             51.719882
## 247             44.697899
## 248             49.333736
## 249             50.836681
## 250             49.497941
## 251             45.822008
## 252             52.106811
## 253             52.704809
## 254             53.400928
## 255             55.899506
## 256             50.787396
## 257             54.235974
## 258             52.259841
## 259             49.279293
## 260             53.377459
## 261             47.441535
## 262             53.523948
## 263             54.794934
## 264             46.131550
## 265             48.774572
## 266             34.966667
## 267             55.172019
## 268             51.928559
## 269             50.121123
## 270             59.094624
## 271             45.520972
## 272             50.382870
## 273             56.373967
## 274             57.079965
## 275             44.901832
## 276             50.711789
## 277             51.742802
## 278             40.299862
## 279             51.522659
## 280             32.164625
## 281             45.401482
## 282             22.998166
## 283             29.123750
## 284             24.963417
## 286             17.109680
## 287             43.216250
## 288             22.925918
## 290             40.580876
## 291             45.240192
## 294             17.039029
## 295             32.163407
## 296             22.710375
## 297             46.547307
## 298             19.967884
## 299             45.749354
## 300             51.161670
## 301             19.068596
## 302             21.326723
## 303             19.489086
## 304             32.392348
## 305             26.058174
## 306             38.482256
## 307             22.232878
## 308             30.021810
## 309             16.660814
## 310             36.575726
## 311             45.466840
## 312             18.477556
## 313             39.062447
## 314             49.173584
## 315             17.200711
## 317             33.843252
## 318             24.292918
## 319             33.009294
## 321             30.924022
## 322             36.384550
## 323             26.212188
## 324             34.875905
## 326             39.558665
## 327             30.713487
## 328             41.843960
## 329             20.290063
## 330             39.930158
## 331             43.315567
## 332             44.759451
## 333             12.888325
## 334             35.542225
## 335             21.513563
## 336             21.741884
## 337             24.584938
## 338             29.130755
## 339             29.902848
## 340             40.393908
## 341             35.643925
## 342             20.719020
## 343             27.695693
## 345             27.494051
## 346             44.251045
## 347             28.966385
## 349             44.510522
## 350             16.772702
## 351             38.367089
## 352             24.286261
## 353             49.685805
## 354             30.443611
## 356             22.889773
## 358             27.058485
## 359             22.787708
## 360             44.825192
## 361             30.436226
## 362             41.504127
## 363             24.967162
## 364             45.303615
## 365             17.811193
## 367             48.185712
## 368             15.811674
## 369             41.758656
## 372             44.079944
## 373             23.700649
## 374             40.866475
## 375             31.034492
## 377             34.966113
## 378             28.762552
## 379             14.106708
## 380             22.336501
## 381             45.570707
## 382             22.844600
## 383             17.530888
## 384             25.226684
## 385             27.198088
## 386             46.555799
## 387             40.305193
## 388             26.685117
## 390             45.995588
## 391             37.812132
## 392             24.134247
## 393             35.459668
## 394             30.976991
## 395             31.791710
## 396             15.349205
## 397             19.433264
## 398             26.786793
## 399             35.379498
## 400             21.898591
## 401             30.784031
## 402             33.368783
## 403             36.711679
## 404             31.481239
## 405             18.255859
## 406             35.610035
## 407             43.530423
## 408             46.650086
## 410             28.555042
## 411             24.120397
## 413             18.502623
## 414             35.284766
## 416             38.025061
## 417             38.961319
## 418             45.561887
## 419             44.248943
## 420             42.446569
## 421             31.184877
## 422             48.674422
## 423             43.123112
## 424             39.700566
## 425             35.760190
## 426             42.794190
## 427             19.481503
## 428             27.702588
## 429             11.808973
## 430             20.566649
## 432             18.701651
## 434             25.499634
## 435             28.152463
## 436             22.803575
## 437             26.008658
## 438             51.391430
## 439             22.686911
## 440             46.333439
## 441             14.106197
## 442             22.055755
## 443             45.862605
## 444             21.683475
## 445             47.478775
## 446             41.710915
## 447             35.066230
## 448             34.849637
## 449             28.475323
## 450             20.532780
## 451             31.908566
## 452             44.376892
## 453             41.564323
## 454             22.128861
## 455             23.008307
## 456             32.758532
## 457             26.301901
## 459             20.811328
## 461             39.406642
## 462             20.341772
## 464             35.723458
## 465             39.169650
## 467             38.809675
## 468             33.370168
## 469             22.614629
## 470             16.537147
## 472             45.616403
## 473             35.730789
## 474             25.571030
## 475             26.875381
## 476             13.755226
## 477             37.562183
## 478             37.592919
## 479             38.214575
## 481             46.962522
## 482             50.682128
## 483             47.721856
## 484             49.069065
## 485             29.333020
## 486             21.635434
## 487             45.641536
## 488             19.346233
## 489             30.002118
## 490             32.543083
## 491             41.058604
## 492             41.627551
## 493             38.184687
## 494             30.179215
## 495             12.566701
## 496             19.940973
## 497             46.585197
## 498             23.682208
## 499             36.217144
## 501             54.911948
## 502             42.233281
## 503             41.774692
## 504             20.778928
## 505             39.235632
## 506             18.895610
## 507             45.023008
## 508             29.351089
## 509             28.679964
## 510             40.942810
## 511             37.442697
## 512             36.105427
## 513             34.829819
## 514             35.248563
## 515             47.629433
## 516             21.051493
## 517             29.349497
## 518             28.061374
## 519             47.619760
## 521             33.863582
## 522             30.868407
## 523             31.733509
## 524             28.712851
## 525             38.880544
## 526             30.458062
## 527             25.608777
## 528             47.670624
## 529             27.426922
## 530             30.555649
## 531             22.954197
## 532             38.104308
## 533             28.822013
## 534             32.236720
## 535             38.552497
## 537             33.278876
## 538             24.702740
## 539             44.915207
## 540             36.721874
## 541             26.120450
## 542             25.815635
## 543             47.940481
## 544             48.883564
## 545             41.137682
## 546             48.150505
## 547             34.586594
## 548             32.265260
## 549             29.297324
## 550             43.871959
## 552             27.687522
## 553             40.914148
## 554             27.286774
## 555             36.307926
## 556             44.411065
## 558             32.336533
## 559             32.214012
## 560             46.566334
## 561             49.560721
## 562             38.343980
## 563             31.910990
## 565             37.858160
## 566             42.153246
## 567             41.077429
## 568             35.956977
## 569             25.630932
## 570             43.990207
## 571             39.662543
## 572             42.729622
## 574             41.362821
## 575             45.568866
## 576             22.490300
## 578             41.591844
## 580             26.837871
## 581             24.067506
## 582             23.301488
## 583             25.569471
## 584             36.756677
## 585             28.630436
## 586             40.597449
## 587             17.452676
## 588             31.922034
## 589             46.500621
## 590             39.775454
## 591             23.158142
## 592             24.791754
## 593             44.768878
## 595             31.924142
## 596             30.074440
## 597             27.354974
## 598             26.580930
## 599             30.723764
## 600             30.516317
## 602             38.595201
## 603             39.096730
## 604             26.626526
## 605             41.909368
## 606             46.146183
## 607             24.459688
## 608             27.892371
## 609             24.438532
## 610             28.688964
## 611             25.119157
## 613             27.380666
## 614             23.610654
## 615             24.670390
## 616             30.497322
## 617             19.061759
## 618             21.618970
## 619             46.202349
## 620             41.450769
## 621             25.068227
## 622             25.891218
## 623             38.937478
## 624             22.605643
## 625             26.519043
## 626             26.802454
## 627             29.326631
## 628             34.020335
## 629             28.589045
## 630             24.384322
## 631             28.537744
## 632             26.157504
## 633             14.158342
## 634             31.571333
## 635             24.573532
## 636             35.255491
## 637             24.482636
## 639             27.853533
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## 110772          50.100314
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## 110774          42.723658
## 110775          46.551957
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## 110777          53.323473
## 110778          54.500459
## 110779          45.722366
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## 110781          52.029122
## 110782          50.760252
## 110783          49.393430
## 110784          59.370394
## 110785          54.476068
## 110786          48.534913
## 110787          49.269358
## 110788          53.115203
## 110790          48.530965
## 110791          56.772989
## 110792          54.448819
## 110793          42.380200
## 110794          48.203114
## 110797          48.914995
## 110798          50.637296
## 110799          49.736397
## 110800          57.916825
## 110801          41.676481
## 110802          43.080373
## 110803          59.082581
## 110804          50.018942
## 110805          55.379923
## 110806          59.462782
## 110807          46.210239
## 110809          55.597309
## 110810          45.466894
## 110811          54.180433
## 110813          47.041528
## 110814          49.428148
## 110815          52.733036
## 110816          54.598922
## 110817          41.890871
## 110819          57.593340
## 110820          43.754651
## 110821          48.022211
## 110822          51.816772
## 110823          55.162231
## 110825          43.097266
## 110827          57.412482
## 110828          51.498419
## 110829          56.458018
## 110830          53.201181
## 110832          52.260281
## 110833          42.689863
## 110834          49.812596
## 110835          44.921519
## 110836          48.470886
## 110837          46.420269
## 110838          52.936961
## 110839          50.530643
## 110841          55.676499
## 110842          52.178075
## 110843          53.036698
## 110844          55.119979
## 110845          48.902804
## 110846          53.328063
## 110847          51.606909
## 110848          49.817499
## 110849          56.324922
## 110850          55.984299
## 110851          48.021661
## 110852          55.157386
## 110853          52.582366
## 110854          38.162131
## 110855          56.515799
## 110857          56.069699
## 110858          52.477655
## 110859          53.216267
## 110860          45.868544
## 110861          53.601721
## 110862          43.837131
## 110864          53.696283
## 110865          48.311483
## 110866          48.793693
## 110867          55.198965
## 110868          57.496614
## 110869          50.023562
## 110870          47.154353
## 110871          39.952257
## 110874          51.060630
## 110875          57.023165
## 110876          50.740499
## 110877          48.162356
## 110878          53.753183
## 110879          55.910859
## 110880          45.611761
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## 110882          54.319785
## 110883          49.429996
## 110884          46.760627
## 110885          53.177263
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## 110890          57.191172
## 110893          27.545067
## 110894          51.146149
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## 110897          55.846552
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## 110903          49.971451
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## 110907          56.519714
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## 110910          56.409297
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## 110913          42.691552
## 110914          29.862164
## 110915          55.985875
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## 110918          54.856176
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## 110922          45.422928
## 110923          40.552642
## 110924          52.951058
## 110925          47.326779
## 110926          49.866028
## 110927          55.337992
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## 110929          51.332929
## 110930          49.492252
## 110931          48.341016
## 110932          54.795064
## 110933          47.221895
## 110934          44.749284
## 110935          51.541273
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## 110938          49.407168
## 110939          50.558254
## 110940          52.126495
## 110941          51.764704
## 110942          50.939481
## 110943          52.104372
## 110945          46.582680
## 110946          58.273722
## 110947          52.472234
## 110948          53.054110
## 110949          50.304249
## 110950          54.687142
## 110951          55.903030
## 110952          55.591762
## 110953          45.981570
## 110955          44.534634
## 110956          51.488720
## 110957          46.188718
## 110958          48.319207
## 110959          50.120150
## 110960          49.593577
## 110961          55.561058
## 110962          48.108976
## 110963          50.734182
## 110964          54.392709
## 110966          49.473709
## 110967          51.315862
## 110968          48.391997
## 110969          53.183385
## 110971          54.530446
## 110972          53.617527
##  [ reached 'max' / getOption("max.print") -- omitted 109454 rows ]
varImpPlot(pop_RF_2,     #<- the randomForest model to use
           sort = TRUE,        #<- whether to sort variables by decreasing order of importance
           n.var = 10,        #<- number of variables to display
           main = "Important Factors for Identifying Song Popularity",
           #cex = 2,           #<- size of characters or symbols
           bg = "white",       #<- background color for the plot
           color = "blue",     #<- color to use for the points and labels
           lcolor = "orange")  #<- color to use for the horizontal lines

Once a final model has been selected (hyper-parameters of the model are set), evaluate the model using the test dataset.

pop_test_RF = randomForest(as.numeric(popularity)~.,          #<- formula, response variable ~ predictors.
                              #   the period means 'use all other variables in the data'.
                              pop_test,     #<- A data frame with variables to be used.
                              #y = NULL,           #<- A response vector. This is unnecessary because we're specifying a response formula.
                              #subset = NULL,      #<- This is unneccessary because we're using all the rows in the training data set.
                              #xtest = NULL,       #<- This is already defined in the formula by the ".".
                              #ytest = NULL,       #<- This is already defined in the formula by "PREGNANT".
                              ntree = 1000,          #<- Number of trees to grow. This should not be set to too small a number, to ensure that every input row gets classified at least a few times.
                              mtry = 5,            #<- Number of variables randomly sampled as candidates at each split. Default number for classification is sqrt(# of variables). Default number for regression is (# of variables / 3).
                              replace = TRUE,      #<- Should sampled data points be replaced.
                              #classwt = NULL,     #<- Priors of the classes. We will work through this later. 
                              #strata = NULL,      #<- Not necessary for our purpose here.
                              sampsize = 10000,      #<- Size of sample to draw each time.
                              nodesize = 5,        #<- Minimum numbers of data points in terminal nodes.
                              #maxnodes = NULL,    #<- The "nodesize" argument limits the number of maximum splits. 
                              importance = TRUE,   #<- Should importance predictors be assessed?
                              #localImp = FALSE,   #<- Should casewise importance measure be computed? (Setting this to TRUE will override importance.)
                              proximity = FALSE,    #<- Should a proximity measure between rows be calculated?
                              norm.votes = TRUE,   #<- If TRUE (default), the final result of votes are expressed as fractions. If FALSE, raw vote counts are returned (useful for combining results from different runs).
                              do.trace = TRUE,     #<- If set to TRUE, give a more verbose output as randomForest is run.
                              keep.forest = TRUE,  #<- If set to FALSE, the forest will not be retained in the output object. If xtest is given, defaults to FALSE.
                              keep.inbag = TRUE)  
##      |      Out-of-bag   |
## Tree |      MSE  %Var(y) |
##    1 |    409.1   124.32 |
##    2 |    353.8   107.51 |
##    3 |    315.2    95.77 |
##    4 |    289.3    87.91 |
##    5 |    270.7    82.26 |
##    6 |    257.9    78.36 |
##    7 |    247.8    75.30 |
##    8 |    241.2    73.29 |
##    9 |    236.5    71.86 |
##   10 |      233    70.81 |
##   11 |    229.9    69.86 |
##   12 |    227.4    69.10 |
##   13 |    225.7    68.60 |
##   14 |    224.1    68.11 |
##   15 |    222.8    67.69 |
##   16 |    221.1    67.20 |
##   17 |    219.7    66.77 |
##   18 |    218.7    66.47 |
##   19 |    217.9    66.22 |
##   20 |    217.4    66.06 |
##   21 |    216.7    65.86 |
##   22 |    215.9    65.61 |
##   23 |    215.4    65.46 |
##   24 |    214.9    65.30 |
##   25 |    214.2    65.10 |
##   26 |    213.8    64.98 |
##   27 |    213.6    64.89 |
##   28 |    213.2    64.79 |
##   29 |    212.9    64.71 |
##   30 |    212.8    64.67 |
##   31 |    212.5    64.58 |
##   32 |    212.1    64.45 |
##   33 |    211.8    64.35 |
##   34 |    211.5    64.28 |
##   35 |    211.3    64.21 |
##   36 |    211.1    64.14 |
##   37 |    210.9    64.08 |
##   38 |    210.7    64.03 |
##   39 |    210.3    63.91 |
##   40 |    210.2    63.88 |
##   41 |    210.1    63.86 |
##   42 |    210.1    63.84 |
##   43 |    209.8    63.74 |
##   44 |    209.5    63.67 |
##   45 |    209.3    63.59 |
##   46 |    209.2    63.56 |
##   47 |      209    63.51 |
##   48 |    208.9    63.48 |
##   49 |    208.8    63.46 |
##   50 |    208.6    63.40 |
##   51 |    208.6    63.38 |
##   52 |    208.3    63.30 |
##   53 |    208.2    63.26 |
##   54 |      208    63.22 |
##   55 |      208    63.19 |
##   56 |    207.8    63.14 |
##   57 |    207.7    63.12 |
##   58 |    207.6    63.07 |
##   59 |    207.5    63.05 |
##   60 |    207.4    63.03 |
##   61 |    207.3    62.98 |
##   62 |    207.2    62.97 |
##   63 |    207.1    62.94 |
##   64 |      207    62.91 |
##   65 |    206.9    62.88 |
##   66 |    206.8    62.83 |
##   67 |    206.7    62.81 |
##   68 |    206.6    62.78 |
##   69 |    206.5    62.75 |
##   70 |    206.4    62.72 |
##   71 |    206.4    62.73 |
##   72 |    206.4    62.71 |
##   73 |    206.3    62.69 |
##   74 |    206.2    62.67 |
##   75 |    206.2    62.67 |
##   76 |    206.1    62.64 |
##   77 |    206.1    62.62 |
##   78 |      206    62.61 |
##   79 |    205.9    62.58 |
##   80 |    205.9    62.56 |
##   81 |    205.8    62.55 |
##   82 |    205.8    62.53 |
##   83 |    205.7    62.50 |
##   84 |    205.7    62.49 |
##   85 |    205.6    62.48 |
##   86 |    205.6    62.46 |
##   87 |    205.5    62.45 |
##   88 |    205.4    62.42 |
##   89 |    205.4    62.42 |
##   90 |    205.4    62.43 |
##   91 |    205.4    62.42 |
##   92 |    205.3    62.39 |
##   93 |    205.3    62.38 |
##   94 |    205.2    62.36 |
##   95 |    205.1    62.34 |
##   96 |    205.1    62.32 |
##   97 |    205.1    62.32 |
##   98 |      205    62.31 |
##   99 |      205    62.28 |
##  100 |    204.9    62.28 |
##  101 |    204.9    62.26 |
##  102 |    204.8    62.25 |
##  103 |    204.8    62.24 |
##  104 |    204.8    62.23 |
##  105 |    204.8    62.22 |
##  106 |    204.6    62.19 |
##  107 |    204.6    62.16 |
##  108 |    204.5    62.16 |
##  109 |    204.5    62.14 |
##  110 |    204.4    62.13 |
##  111 |    204.4    62.11 |
##  112 |    204.4    62.11 |
##  113 |    204.3    62.10 |
##  114 |    204.3    62.08 |
##  115 |    204.2    62.06 |
##  116 |    204.2    62.06 |
##  117 |    204.2    62.05 |
##  118 |    204.2    62.04 |
##  119 |    204.1    62.04 |
##  120 |    204.1    62.02 |
##  121 |    204.1    62.02 |
##  122 |    204.1    62.01 |
##  123 |    204.1    62.01 |
##  124 |      204    61.99 |
##  125 |      204    61.99 |
##  126 |      204    61.98 |
##  127 |    203.9    61.97 |
##  128 |    203.9    61.95 |
##  129 |    203.8    61.94 |
##  130 |    203.8    61.93 |
##  131 |    203.8    61.92 |
##  132 |    203.7    61.91 |
##  133 |    203.7    61.91 |
##  134 |    203.7    61.91 |
##  135 |    203.7    61.90 |
##  136 |    203.7    61.89 |
##  137 |    203.6    61.88 |
##  138 |    203.6    61.87 |
##  139 |    203.6    61.87 |
##  140 |    203.5    61.85 |
##  141 |    203.5    61.85 |
##  142 |    203.5    61.85 |
##  143 |    203.5    61.84 |
##  144 |    203.5    61.84 |
##  145 |    203.5    61.84 |
##  146 |    203.5    61.84 |
##  147 |    203.5    61.84 |
##  148 |    203.5    61.83 |
##  149 |    203.5    61.83 |
##  150 |    203.5    61.84 |
##  151 |    203.5    61.83 |
##  152 |    203.5    61.83 |
##  153 |    203.4    61.82 |
##  154 |    203.4    61.82 |
##  155 |    203.4    61.81 |
##  156 |    203.4    61.80 |
##  157 |    203.4    61.80 |
##  158 |    203.4    61.80 |
##  159 |    203.3    61.79 |
##  160 |    203.4    61.79 |
##  161 |    203.3    61.79 |
##  162 |    203.3    61.79 |
##  163 |    203.3    61.79 |
##  164 |    203.3    61.78 |
##  165 |    203.3    61.79 |
##  166 |    203.3    61.78 |
##  167 |    203.3    61.78 |
##  168 |    203.3    61.78 |
##  169 |    203.3    61.78 |
##  170 |    203.3    61.78 |
##  171 |    203.3    61.77 |
##  172 |    203.3    61.77 |
##  173 |    203.3    61.78 |
##  174 |    203.3    61.77 |
##  175 |    203.3    61.77 |
##  176 |    203.3    61.78 |
##  177 |    203.3    61.78 |
##  178 |    203.3    61.78 |
##  179 |    203.3    61.78 |
##  180 |    203.3    61.78 |
##  181 |    203.3    61.78 |
##  182 |    203.3    61.78 |
##  183 |    203.3    61.78 |
##  184 |    203.3    61.77 |
##  185 |    203.2    61.76 |
##  186 |    203.3    61.77 |
##  187 |    203.3    61.77 |
##  188 |    203.3    61.77 |
##  189 |    203.3    61.77 |
##  190 |    203.3    61.77 |
##  191 |    203.3    61.77 |
##  192 |    203.3    61.76 |
##  193 |    203.2    61.76 |
##  194 |    203.2    61.76 |
##  195 |    203.2    61.75 |
##  196 |    203.2    61.76 |
##  197 |    203.2    61.75 |
##  198 |    203.2    61.75 |
##  199 |    203.2    61.75 |
##  200 |    203.2    61.75 |
##  201 |    203.2    61.74 |
##  202 |    203.2    61.74 |
##  203 |    203.2    61.74 |
##  204 |    203.2    61.74 |
##  205 |    203.2    61.74 |
##  206 |    203.2    61.74 |
##  207 |    203.2    61.74 |
##  208 |    203.1    61.73 |
##  209 |    203.1    61.72 |
##  210 |    203.1    61.72 |
##  211 |    203.1    61.71 |
##  212 |    203.1    61.71 |
##  213 |    203.1    61.71 |
##  214 |    203.1    61.71 |
##  215 |    203.1    61.71 |
##  216 |    203.1    61.71 |
##  217 |      203    61.69 |
##  218 |      203    61.70 |
##  219 |      203    61.70 |
##  220 |      203    61.69 |
##  221 |      203    61.69 |
##  222 |      203    61.69 |
##  223 |      203    61.69 |
##  224 |      203    61.68 |
##  225 |      203    61.68 |
##  226 |      203    61.67 |
##  227 |      203    61.68 |
##  228 |    202.9    61.67 |
##  229 |    202.9    61.67 |
##  230 |      203    61.67 |
##  231 |    202.9    61.67 |
##  232 |    202.9    61.66 |
##  233 |    202.9    61.66 |
##  234 |    202.9    61.66 |
##  235 |    202.9    61.66 |
##  236 |    202.9    61.66 |
##  237 |    202.9    61.65 |
##  238 |    202.9    61.65 |
##  239 |    202.9    61.64 |
##  240 |    202.8    61.64 |
##  241 |    202.8    61.64 |
##  242 |    202.8    61.63 |
##  243 |    202.8    61.63 |
##  244 |    202.8    61.64 |
##  245 |    202.8    61.64 |
##  246 |    202.8    61.64 |
##  247 |    202.9    61.65 |
##  248 |    202.9    61.64 |
##  249 |    202.9    61.64 |
##  250 |    202.8    61.64 |
##  251 |    202.9    61.65 |
##  252 |    202.9    61.64 |
##  253 |    202.9    61.64 |
##  254 |    202.8    61.64 |
##  255 |    202.8    61.64 |
##  256 |    202.8    61.64 |
##  257 |    202.8    61.64 |
##  258 |    202.8    61.64 |
##  259 |    202.8    61.64 |
##  260 |    202.9    61.65 |
##  261 |    202.9    61.65 |
##  262 |    202.9    61.65 |
##  263 |    202.9    61.64 |
##  264 |    202.9    61.64 |
##  265 |    202.9    61.65 |
##  266 |    202.9    61.65 |
##  267 |    202.9    61.65 |
##  268 |    202.8    61.64 |
##  269 |    202.8    61.63 |
##  270 |    202.8    61.63 |
##  271 |    202.8    61.63 |
##  272 |    202.8    61.62 |
##  273 |    202.8    61.62 |
##  274 |    202.8    61.62 |
##  275 |    202.8    61.61 |
##  276 |    202.8    61.62 |
##  277 |    202.7    61.61 |
##  278 |    202.7    61.61 |
##  279 |    202.7    61.60 |
##  280 |    202.7    61.60 |
##  281 |    202.7    61.60 |
##  282 |    202.7    61.60 |
##  283 |    202.7    61.60 |
##  284 |    202.7    61.59 |
##  285 |    202.7    61.60 |
##  286 |    202.7    61.59 |
##  287 |    202.7    61.59 |
##  288 |    202.7    61.60 |
##  289 |    202.7    61.60 |
##  290 |    202.7    61.59 |
##  291 |    202.7    61.60 |
##  292 |    202.7    61.60 |
##  293 |    202.7    61.60 |
##  294 |    202.7    61.59 |
##  295 |    202.7    61.59 |
##  296 |    202.7    61.58 |
##  297 |    202.7    61.58 |
##  298 |    202.7    61.58 |
##  299 |    202.6    61.58 |
##  300 |    202.6    61.58 |
##  301 |    202.7    61.58 |
##  302 |    202.6    61.57 |
##  303 |    202.6    61.58 |
##  304 |    202.6    61.58 |
##  305 |    202.6    61.58 |
##  306 |    202.7    61.58 |
##  307 |    202.7    61.58 |
##  308 |    202.6    61.58 |
##  309 |    202.6    61.58 |
##  310 |    202.6    61.58 |
##  311 |    202.7    61.58 |
##  312 |    202.7    61.59 |
##  313 |    202.7    61.59 |
##  314 |    202.7    61.59 |
##  315 |    202.7    61.59 |
##  316 |    202.7    61.58 |
##  317 |    202.7    61.58 |
##  318 |    202.7    61.59 |
##  319 |    202.7    61.59 |
##  320 |    202.6    61.58 |
##  321 |    202.6    61.58 |
##  322 |    202.6    61.58 |
##  323 |    202.7    61.58 |
##  324 |    202.7    61.58 |
##  325 |    202.7    61.58 |
##  326 |    202.7    61.58 |
##  327 |    202.7    61.59 |
##  328 |    202.7    61.58 |
##  329 |    202.6    61.58 |
##  330 |    202.6    61.58 |
##  331 |    202.6    61.58 |
##  332 |    202.6    61.57 |
##  333 |    202.6    61.58 |
##  334 |    202.6    61.58 |
##  335 |    202.6    61.57 |
##  336 |    202.6    61.57 |
##  337 |    202.6    61.57 |
##  338 |    202.6    61.57 |
##  339 |    202.6    61.57 |
##  340 |    202.6    61.57 |
##  341 |    202.6    61.57 |
##  342 |    202.6    61.57 |
##  343 |    202.6    61.57 |
##  344 |    202.6    61.57 |
##  345 |    202.6    61.56 |
##  346 |    202.6    61.56 |
##  347 |    202.6    61.56 |
##  348 |    202.6    61.56 |
##  349 |    202.6    61.56 |
##  350 |    202.6    61.55 |
##  351 |    202.6    61.55 |
##  352 |    202.6    61.55 |
##  353 |    202.6    61.55 |
##  354 |    202.6    61.55 |
##  355 |    202.5    61.55 |
##  356 |    202.5    61.55 |
##  357 |    202.5    61.55 |
##  358 |    202.5    61.55 |
##  359 |    202.5    61.55 |
##  360 |    202.5    61.55 |
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##  929 |    201.9    61.35 |
##  930 |    201.9    61.35 |
##  931 |    201.9    61.35 |
##  932 |    201.9    61.35 |
##  933 |    201.9    61.35 |
##  934 |    201.9    61.35 |
##  935 |    201.9    61.35 |
##  936 |    201.9    61.35 |
##  937 |    201.9    61.35 |
##  938 |    201.9    61.35 |
##  939 |    201.9    61.35 |
##  940 |    201.9    61.35 |
##  941 |    201.9    61.35 |
##  942 |    201.9    61.35 |
##  943 |    201.9    61.35 |
##  944 |    201.9    61.35 |
##  945 |    201.9    61.35 |
##  946 |    201.9    61.35 |
##  947 |    201.9    61.35 |
##  948 |    201.9    61.35 |
##  949 |    201.9    61.35 |
##  950 |    201.9    61.35 |
##  951 |    201.9    61.35 |
##  952 |    201.9    61.35 |
##  953 |    201.9    61.35 |
##  954 |    201.9    61.35 |
##  955 |    201.9    61.35 |
##  956 |    201.9    61.35 |
##  957 |    201.9    61.35 |
##  958 |    201.9    61.35 |
##  959 |    201.9    61.35 |
##  960 |    201.9    61.35 |
##  961 |    201.9    61.35 |
##  962 |    201.9    61.35 |
##  963 |    201.9    61.35 |
##  964 |    201.9    61.35 |
##  965 |    201.9    61.35 |
##  966 |    201.9    61.35 |
##  967 |    201.9    61.35 |
##  968 |    201.9    61.35 |
##  969 |    201.9    61.35 |
##  970 |    201.9    61.35 |
##  971 |    201.9    61.35 |
##  972 |    201.9    61.35 |
##  973 |    201.9    61.35 |
##  974 |    201.9    61.35 |
##  975 |    201.9    61.36 |
##  976 |    201.9    61.35 |
##  977 |    201.9    61.36 |
##  978 |    201.9    61.36 |
##  979 |    201.9    61.36 |
##  980 |    201.9    61.36 |
##  981 |    201.9    61.36 |
##  982 |    201.9    61.36 |
##  983 |    201.9    61.36 |
##  984 |    201.9    61.36 |
##  985 |    201.9    61.36 |
##  986 |    201.9    61.36 |
##  987 |    201.9    61.36 |
##  988 |    201.9    61.36 |
##  989 |    201.9    61.36 |
##  990 |    201.9    61.36 |
##  991 |    201.9    61.36 |
##  992 |    201.9    61.36 |
##  993 |    201.9    61.36 |
##  994 |    201.9    61.36 |
##  995 |    201.9    61.36 |
##  996 |    201.9    61.36 |
##  997 |    201.9    61.36 |
##  998 |    201.9    61.36 |
##  999 |    201.9    61.36 |
## 1000 |    201.9    61.36 |
pop_test_RF
## 
## Call:
##  randomForest(formula = as.numeric(popularity) ~ ., data = pop_test,      ntree = 1000, mtry = 5, replace = TRUE, sampsize = 10000,      nodesize = 5, importance = TRUE, proximity = FALSE, norm.votes = TRUE,      do.trace = TRUE, keep.forest = TRUE, keep.inbag = TRUE) 
##                Type of random forest: regression
##                      Number of trees: 1000
## No. of variables tried at each split: 5
## 
##           Mean of squared residuals: 201.9207
##                     % Var explained: 38.64
sqrt(pop_test_RF$mse[length(pop_test_RF$mse)])
## [1] 14.20988
as.data.frame(pop_test_RF$predicted)
##        pop_test_RF$predicted
## 225246             41.888839
## 218298             35.363979
## 56533              51.472522
## 94880              50.916491
## 145135             43.276299
## 197393             37.335999
## 47172              41.215990
## 198097             29.196251
## 144557             43.493163
## 202                48.614612
## 121794             48.487494
## 10326              51.853051
## 103637             44.428611
## 25000              38.788665
## 116635             50.852761
## 224331             50.184893
## 85425              42.036854
## 15030              55.033876
## 214810             49.559949
## 221500             25.094650
## 29192              31.177736
## 173247             22.691951
## 76104              23.254192
## 140116             56.129895
## 201325             33.052234
## 66460              43.483205
## 19034              43.121414
## 148299             36.852501
## 116064             51.048383
## 143101             40.907879
## 94527              43.645156
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## 191471             31.447548
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varImpPlot(pop_test_RF,     #<- the randomForest model to use
           sort = TRUE,        #<- whether to sort variables by decreasing order of importance
           n.var = 10,        #<- number of variables to display
           main = "Important Factors for Identifying Song Popularity",
           #cex = 2,           #<- size of characters or symbols
           bg = "white",       #<- background color for the plot
           color = "blue",     #<- color to use for the points and labels
           lcolor = "orange")  #<- color to use for the horizontal lines